Prealgebra & Introductory Algebra (4th Edition)
4th Edition
ISBN: 9780321955791
Author: Elayn Martin-Gay
Publisher: PEARSON
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Question
Chapter 10.CR, Problem 125CR
To determine
To simplify:
The expression,
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Students have asked these similar questions
1. True or false:
(a) if E is a subspace of V, then dim(E) + dim(E+) = dim(V)
(b) Let {i, n} be a basis of the vector space V, where vi,..., are all eigen-
vectors for both the matrix A and the matrix B. Then, any eigenvector of A is
an eigenvector of B.
Justify.
2. Apply Gram-Schmidt orthogonalization to the system of vectors {(1, 2, -2), (1, −1, 4), (2, 1, 1)}.
3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal
projection onto the orthogonal complement E.
(a) The combinations of projections P+Q and PQ correspond to well-known oper-
ators. What are they? Justify your answer.
(b) Show that P - Q is its own inverse.
4. Show that the Frobenius product on n x n-matrices,
(A, B) =
= Tr(B*A),
is an inner product, where B* denotes the Hermitian adjoint of B.
5. Show that if A and B are two n x n-matrices for which {1,..., n} is a basis of eigen-
vectors (for both A and B), then AB = BA.
Remark: It is also true that if AB = BA, then there exists a common…
Question 1. Let f: XY and g: Y Z be two functions. Prove that
(1) if go f is injective, then f is injective;
(2) if go f is surjective, then g is surjective.
Question 2. Prove or disprove:
(1) The set X = {k € Z} is countable.
(2) The set X = {k EZ,nЄN} is countable.
(3) The set X = R\Q = {x ER2
countable.
Q} (the set of all irrational numbers) is
(4) The set X = {p.√2pQ} is countable.
(5) The interval X = [0,1] is countable.
Question 3. Let X = {f|f: N→ N}, the set of all functions from N to N. Prove
that X is uncountable.
Extra practice (not to be submitted).
Question. Prove the following by induction.
(1) For any nЄN, 1+3+5++2n-1 n².
(2) For any nЄ N, 1+2+3++ n = n(n+1).
Question. Write explicitly a function f: Nx N N which is bijective.
3. Suppose P is the orthogonal projection onto a subspace E, and Q is the orthogonal
projection onto the orthogonal complement E.
(a) The combinations of projections P+Q and PQ correspond to well-known oper-
ators. What are they? Justify your answer.
(b) Show that P - Q is its own inverse.
Chapter 10 Solutions
Prealgebra & Introductory Algebra (4th Edition)
Ch. 10.1 - Prob. 1CCCh. 10.1 - Prob. 2CCCh. 10.1 - Prob. 1PCh. 10.1 - Prob. 2PCh. 10.1 - Prob. 3PCh. 10.1 - Prob. 4PCh. 10.1 - Prob. 5PCh. 10.1 - Prob. 6PCh. 10.1 - Prob. 7PCh. 10.1 - Prob. 8P
Ch. 10.1 - Prob. 9PCh. 10.1 - Prob. 10PCh. 10.1 - Prob. 11PCh. 10.1 - Prob. 12PCh. 10.1 - Prob. 13PCh. 10.1 - Prob. 14PCh. 10.1 - Prob. 15PCh. 10.1 - Prob. 16PCh. 10.1 - Prob. 17PCh. 10.1 - Prob. 18PCh. 10.1 - Prob. 19PCh. 10.1 - Prob. 20PCh. 10.1 - Prob. 21PCh. 10.1 - Prob. 22PCh. 10.1 - Prob. 23PCh. 10.1 - Prob. 24PCh. 10.1 - Prob. 25PCh. 10.1 - Prob. 26PCh. 10.1 - Prob. 27PCh. 10.1 - Prob. 28PCh. 10.1 - Prob. 29PCh. 10.1 - Prob. 30PCh. 10.1 - Prob. 31PCh. 10.1 - Prob. 32PCh. 10.1 - Prob. 33PCh. 10.1 - Prob. 1VRVCCh. 10.1 - Prob. 2VRVCCh. 10.1 - Prob. 3VRVCCh. 10.1 - Prob. 4VRVCCh. 10.1 - Prob. 5VRVCCh. 10.1 - Prob. 6VRVCCh. 10.1 - Prob. 7VRVCCh. 10.1 - Prob. 8VRVCCh. 10.1 - Prob. 9VRVCCh. 10.1 - Prob. 10VRVCCh. 10.1 - Prob. 11VRVCCh. 10.1 - Prob. 12VRVCCh. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Prob. 37ECh. 10.1 - Prob. 38ECh. 10.1 - Prob. 39ECh. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - Prob. 42ECh. 10.1 - Prob. 43ECh. 10.1 - Prob. 44ECh. 10.1 - Prob. 45ECh. 10.1 - Prob. 46ECh. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - Prob. 49ECh. 10.1 - Prob. 50ECh. 10.1 - Prob. 51ECh. 10.1 - Prob. 52ECh. 10.1 - Prob. 53ECh. 10.1 - Prob. 54ECh. 10.1 - Prob. 55ECh. 10.1 - Prob. 56ECh. 10.1 - Prob. 57ECh. 10.1 - Prob. 58ECh. 10.1 - Prob. 59ECh. 10.1 - Prob. 60ECh. 10.1 - Prob. 61ECh. 10.1 - Prob. 62ECh. 10.1 - 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Prob. 113ECh. 10.1 - Prob. 114ECh. 10.1 - Prob. 115ECh. 10.1 - Prob. 116ECh. 10.1 - Prob. 117ECh. 10.1 - Prob. 118ECh. 10.1 - Prob. 119ECh. 10.1 - Prob. 120ECh. 10.1 - Prob. 121ECh. 10.1 - Prob. 122ECh. 10.1 - Prob. 123ECh. 10.1 - Prob. 124ECh. 10.1 - Prob. 125ECh. 10.1 - Prob. 126ECh. 10.1 - Prob. 127ECh. 10.1 - Prob. 128ECh. 10.1 - Prob. 129ECh. 10.1 - Prob. 130ECh. 10.1 - Prob. 131ECh. 10.1 - Prob. 132ECh. 10.2 - Prob. 1CCCh. 10.2 - Prob. 1PCh. 10.2 - Prob. 2PCh. 10.2 - Prob. 3PCh. 10.2 - Prob. 4PCh. 10.2 - Prob. 5PCh. 10.2 - Prob. 6PCh. 10.2 - Prob. 7PCh. 10.2 - Prob. 8PCh. 10.2 - Prob. 9PCh. 10.2 - Prob. 10PCh. 10.2 - Prob. 11PCh. 10.2 - Prob. 12PCh. 10.2 - Prob. 13PCh. 10.2 - Prob. 14PCh. 10.2 - Prob. 15PCh. 10.2 - Prob. 16PCh. 10.2 - Prob. 17PCh. 10.2 - Prob. 18PCh. 10.2 - Prob. 19PCh. 10.2 - Prob. 1VRVCCh. 10.2 - Prob. 2VRVCCh. 10.2 - Prob. 3VRVCCh. 10.2 - Prob. 4VRVCCh. 10.2 - Prob. 5VRVCCh. 10.2 - Prob. 6VRVCCh. 10.2 - Prob. 7VRVCCh. 10.2 - Prob. 8VRVCCh. 10.2 - Prob. 9VRVCCh. 10.2 - Prob. 10VRVCCh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Prob. 41ECh. 10.2 - Prob. 42ECh. 10.2 - Prob. 43ECh. 10.2 - Prob. 44ECh. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Prob. 49ECh. 10.2 - Prob. 50ECh. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Prob. 53ECh. 10.2 - Prob. 54ECh. 10.2 - Prob. 55ECh. 10.2 - Prob. 56ECh. 10.2 - Prob. 57ECh. 10.2 - Prob. 58ECh. 10.2 - Prob. 59ECh. 10.2 - Prob. 60ECh. 10.2 - Prob. 61ECh. 10.2 - Prob. 62ECh. 10.2 - Prob. 63ECh. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Prob. 66ECh. 10.2 - Prob. 67ECh. 10.2 - Prob. 68ECh. 10.2 - Prob. 69ECh. 10.2 - Prob. 70ECh. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.2 - Prob. 73ECh. 10.2 - Prob. 74ECh. 10.2 - Prob. 75ECh. 10.2 - Prob. 76ECh. 10.2 - Prob. 77ECh. 10.2 - Prob. 78ECh. 10.2 - Prob. 79ECh. 10.2 - Prob. 80ECh. 10.2 - Prob. 81ECh. 10.2 - Prob. 82ECh. 10.2 - Prob. 83ECh. 10.2 - Prob. 84ECh. 10.2 - Prob. 85ECh. 10.2 - Prob. 86ECh. 10.2 - Prob. 87ECh. 10.2 - Prob. 88ECh. 10.2 - Prob. 89ECh. 10.2 - Prob. 90ECh. 10.2 - Prob. 91ECh. 10.2 - Prob. 92ECh. 10.2 - Prob. 93ECh. 10.2 - Prob. 94ECh. 10.2 - Prob. 95ECh. 10.2 - Prob. 96ECh. 10.2 - Prob. 97ECh. 10.2 - Prob. 98ECh. 10.2 - Prob. 99ECh. 10.2 - Prob. 100ECh. 10.2 - Prob. 101ECh. 10.2 - Prob. 102ECh. 10.2 - Prob. 103ECh. 10.2 - Prob. 104ECh. 10.2 - Prob. 105ECh. 10.2 - Prob. 106ECh. 10.2 - Prob. 107ECh. 10.2 - Prob. 108ECh. 10.2 - Prob. 109ECh. 10.2 - Prob. 110ECh. 10.2 - Prob. 111ECh. 10.2 - Prob. 112ECh. 10.2 - Prob. 113ECh. 10.2 - Prob. 114ECh. 10.2 - Prob. 115ECh. 10.2 - Prob. 116ECh. 10.2 - Prob. 117ECh. 10.2 - Prob. 118ECh. 10.2 - Prob. 119ECh. 10.2 - Prob. 120ECh. 10.2 - Prob. 121ECh. 10.2 - Prob. 122ECh. 10.2 - Prob. 123ECh. 10.2 - Prob. 124ECh. 10.2 - Prob. 125ECh. 10.2 - Prob. 126ECh. 10.2 - Prob. 127ECh. 10.2 - Prob. 128ECh. 10.2 - Prob. 129ECh. 10.2 - Prob. 130ECh. 10.2 - Prob. 131ECh. 10.2 - Prob. 132ECh. 10.2 - Prob. 133ECh. 10.2 - Prob. 134ECh. 10.2 - Prob. 1CECh. 10.2 - Prob. 2CECh. 10.2 - Prob. 3CECh. 10.2 - Prob. 4CECh. 10.2 - Prob. 5CECh. 10.2 - Prob. 6CECh. 10.2 - Prob. 7CECh. 10.2 - Prob. 8CECh. 10.3 - Prob. 1PCh. 10.3 - Prob. 2PCh. 10.3 - Prob. 3PCh. 10.3 - Prob. 4PCh. 10.3 - Prob. 5PCh. 10.3 - Prob. 6PCh. 10.3 - Prob. 7PCh. 10.3 - Prob. 8PCh. 10.3 - Prob. 9PCh. 10.3 - Prob. 10PCh. 10.3 - Prob. 11PCh. 10.3 - Prob. 12PCh. 10.3 - Prob. 13PCh. 10.3 - Prob. 14PCh. 10.3 - Prob. 15PCh. 10.3 - Prob. 1VRVCCh. 10.3 - Prob. 2VRVCCh. 10.3 - Prob. 3VRVCCh. 10.3 - Prob. 4VRVCCh. 10.3 - Prob. 5VRVCCh. 10.3 - Prob. 6VRVCCh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Prob. 46ECh. 10.3 - Prob. 47ECh. 10.3 - Prob. 48ECh. 10.3 - Prob. 49ECh. 10.3 - Prob. 50ECh. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Prob. 53ECh. 10.3 - Prob. 54ECh. 10.3 - Prob. 55ECh. 10.3 - Prob. 56ECh. 10.3 - Prob. 57ECh. 10.3 - Prob. 58ECh. 10.3 - Prob. 59ECh. 10.3 - Prob. 60ECh. 10.3 - Prob. 61ECh. 10.3 - Prob. 62ECh. 10.3 - Prob. 63ECh. 10.3 - Prob. 64ECh. 10.3 - Prob. 65ECh. 10.3 - Prob. 66ECh. 10.3 - Prob. 67ECh. 10.3 - Prob. 68ECh. 10.3 - Prob. 69ECh. 10.3 - Prob. 70ECh. 10.3 - Prob. 71ECh. 10.3 - Prob. 72ECh. 10.3 - Prob. 73ECh. 10.3 - Prob. 74ECh. 10.3 - Prob. 75ECh. 10.3 - Prob. 76ECh. 10.3 - Prob. 77ECh. 10.3 - Prob. 78ECh. 10.3 - Prob. 79ECh. 10.3 - Prob. 80ECh. 10.3 - Prob. 81ECh. 10.3 - Prob. 82ECh. 10.3 - Prob. 83ECh. 10.3 - Prob. 84ECh. 10.3 - Prob. 85ECh. 10.3 - Prob. 86ECh. 10.3 - Prob. 87ECh. 10.3 - Prob. 88ECh. 10.4 - Prob. 1CCCh. 10.4 - Prob. 2CCCh. 10.4 - Prob. 1PCh. 10.4 - Prob. 2PCh. 10.4 - Prob. 3PCh. 10.4 - Prob. 4PCh. 10.4 - Prob. 5PCh. 10.4 - Prob. 6PCh. 10.4 - Prob. 7PCh. 10.4 - Prob. 8PCh. 10.4 - Prob. 9PCh. 10.4 - Prob. 1VRVCCh. 10.4 - Prob. 2VRVCCh. 10.4 - Prob. 3VRVCCh. 10.4 - Prob. 4VRVCCh. 10.4 - Prob. 5VRVCCh. 10.4 - Prob. 6VRVCCh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Prob. 59ECh. 10.4 - Prob. 60ECh. 10.4 - Prob. 61ECh. 10.4 - Prob. 62ECh. 10.4 - Prob. 63ECh. 10.4 - Prob. 64ECh. 10.4 - Prob. 65ECh. 10.4 - Prob. 66ECh. 10.4 - Prob. 67ECh. 10.4 - Prob. 68ECh. 10.4 - Prob. 69ECh. 10.4 - Prob. 70ECh. 10.4 - Prob. 71ECh. 10.4 - Prob. 72ECh. 10.4 - Prob. 73ECh. 10.4 - Prob. 74ECh. 10.4 - Prob. 75ECh. 10.4 - Prob. 76ECh. 10.4 - Prob. 77ECh. 10.4 - Prob. 78ECh. 10.4 - Prob. 79ECh. 10.4 - Prob. 80ECh. 10.4 - Prob. 81ECh. 10.4 - Prob. 82ECh. 10.4 - 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Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Prob. 42ECh. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - Prob. 45ECh. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Prob. 50ECh. 10.5 - Prob. 51ECh. 10.5 - Prob. 52ECh. 10.5 - Prob. 53ECh. 10.5 - Prob. 54ECh. 10.5 - Prob. 55ECh. 10.5 - Prob. 56ECh. 10.5 - Prob. 57ECh. 10.5 - Prob. 58ECh. 10.5 - Prob. 59ECh. 10.5 - Prob. 60ECh. 10.5 - Prob. 61ECh. 10.5 - Prob. 62ECh. 10.5 - Prob. 63ECh. 10.5 - Prob. 64ECh. 10.5 - Prob. 65ECh. 10.5 - Prob. 66ECh. 10.5 - Prob. 67ECh. 10.5 - Prob. 68ECh. 10.5 - Prob. 69ECh. 10.5 - Prob. 70ECh. 10.5 - Prob. 71ECh. 10.5 - Prob. 72ECh. 10.5 - Prob. 73ECh. 10.5 - Prob. 74ECh. 10.5 - Prob. 75ECh. 10.5 - Prob. 76ECh. 10.5 - Prob. 77ECh. 10.5 - Prob. 78ECh. 10.5 - Prob. 79ECh. 10.5 - Prob. 80ECh. 10.5 - Prob. 81ECh. 10.5 - Prob. 82ECh. 10.5 - Prob. 83ECh. 10.5 - Prob. 84ECh. 10.5 - Prob. 85ECh. 10.5 - Prob. 86ECh. 10.5 - Prob. 87ECh. 10.5 - Prob. 88ECh. 10.5 - Prob. 89ECh. 10.5 - Prob. 90ECh. 10.5 - Prob. 91ECh. 10.5 - Prob. 92ECh. 10.5 - Prob. 93ECh. 10.5 - Prob. 94ECh. 10.5 - Prob. 95ECh. 10.5 - Prob. 96ECh. 10.6 - Prob. 1CCCh. 10.6 - Prob. 1PCh. 10.6 - Prob. 2PCh. 10.6 - Prob. 3PCh. 10.6 - Prob. 4PCh. 10.6 - Prob. 5PCh. 10.6 - Prob. 6PCh. 10.6 - Prob. 7PCh. 10.6 - Prob. 8PCh. 10.6 - Prob. 9PCh. 10.6 - Prob. 10PCh. 10.6 - Prob. 11PCh. 10.6 - Prob. 12PCh. 10.6 - Prob. 13PCh. 10.6 - Prob. 14PCh. 10.6 - Prob. 15PCh. 10.6 - Prob. 16PCh. 10.6 - Prob. 17PCh. 10.6 - Prob. 1VRVCCh. 10.6 - Prob. 2VRVCCh. 10.6 - Prob. 3VRVCCh. 10.6 - Prob. 4VRVCCh. 10.6 - Prob. 1ECh. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.6 - Prob. 7ECh. 10.6 - Prob. 8ECh. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - Prob. 18ECh. 10.6 - Prob. 19ECh. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - Prob. 23ECh. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - Prob. 27ECh. 10.6 - Prob. 28ECh. 10.6 - Prob. 29ECh. 10.6 - Prob. 30ECh. 10.6 - Prob. 31ECh. 10.6 - Prob. 32ECh. 10.6 - Prob. 33ECh. 10.6 - Prob. 34ECh. 10.6 - Prob. 35ECh. 10.6 - Prob. 36ECh. 10.6 - Prob. 37ECh. 10.6 - Prob. 38ECh. 10.6 - Prob. 39ECh. 10.6 - Prob. 40ECh. 10.6 - Prob. 41ECh. 10.6 - Prob. 42ECh. 10.6 - Prob. 43ECh. 10.6 - Prob. 44ECh. 10.6 - Prob. 45ECh. 10.6 - Prob. 46ECh. 10.6 - Prob. 47ECh. 10.6 - Prob. 48ECh. 10.6 - Prob. 49ECh. 10.6 - Prob. 50ECh. 10.6 - Prob. 51ECh. 10.6 - Prob. 52ECh. 10.6 - Prob. 53ECh. 10.6 - Prob. 54ECh. 10.6 - Prob. 55ECh. 10.6 - Prob. 56ECh. 10.6 - Prob. 57ECh. 10.6 - Prob. 58ECh. 10.6 - Prob. 59ECh. 10.6 - Prob. 60ECh. 10.6 - Prob. 61ECh. 10.6 - Prob. 62ECh. 10.6 - Prob. 63ECh. 10.6 - Prob. 64ECh. 10.6 - Prob. 65ECh. 10.6 - Prob. 66ECh. 10.6 - Prob. 67ECh. 10.6 - Prob. 68ECh. 10.6 - Prob. 69ECh. 10.6 - Prob. 70ECh. 10.6 - Prob. 71ECh. 10.6 - Prob. 72ECh. 10.6 - Prob. 73ECh. 10.6 - Prob. 74ECh. 10.6 - Prob. 75ECh. 10.6 - Prob. 76ECh. 10.6 - Prob. 77ECh. 10.6 - Prob. 78ECh. 10.6 - Prob. 79ECh. 10.6 - Prob. 80ECh. 10.6 - Prob. 81ECh. 10.6 - Prob. 82ECh. 10.6 - Prob. 83ECh. 10.6 - Prob. 84ECh. 10.6 - Prob. 85ECh. 10.6 - Prob. 86ECh. 10.6 - Prob. 87ECh. 10.6 - Prob. 88ECh. 10.6 - Prob. 89ECh. 10.6 - Prob. 90ECh. 10.6 - Prob. 91ECh. 10.6 - Prob. 92ECh. 10.6 - Prob. 93ECh. 10.6 - Prob. 94ECh. 10.6 - Prob. 95ECh. 10.6 - Prob. 96ECh. 10.6 - Prob. 97ECh. 10.6 - Prob. 98ECh. 10.6 - Prob. 99ECh. 10.6 - Prob. 100ECh. 10.6 - Prob. 101ECh. 10.6 - Prob. 102ECh. 10.IR - Prob. 1IRCh. 10.IR - Prob. 2IRCh. 10.IR - Prob. 3IRCh. 10.IR - Prob. 4IRCh. 10.IR - Prob. 5IRCh. 10.IR - Prob. 6IRCh. 10.IR - Prob. 7IRCh. 10.IR - Prob. 8IRCh. 10.IR - Prob. 9IRCh. 10.IR - Prob. 10IRCh. 10.IR - Prob. 11IRCh. 10.IR - Prob. 12IRCh. 10.IR - Prob. 13IRCh. 10.IR - Prob. 14IRCh. 10.IR - Prob. 15IRCh. 10.IR - Prob. 16IRCh. 10.IR - Prob. 17IRCh. 10.IR - Prob. 18IRCh. 10.IR - Prob. 19IRCh. 10.IR - Prob. 20IRCh. 10.IR - Prob. 21IRCh. 10.IR - Prob. 22IRCh. 10.IR - Prob. 23IRCh. 10.IR - Prob. 24IRCh. 10.IR - Prob. 25IRCh. 10.IR - Prob. 26IRCh. 10.IR - Prob. 27IRCh. 10.IR - Prob. 28IRCh. 10.IR - Prob. 29IRCh. 10.IR - Prob. 30IRCh. 10.IR - Prob. 31IRCh. 10.IR - Prob. 32IRCh. 10.IR - Prob. 33IRCh. 10.IR - Prob. 34IRCh. 10.IR - Prob. 35IRCh. 10.IR - Prob. 36IRCh. 10.IR - Prob. 37IRCh. 10.IR - Prob. 38IRCh. 10.7 - Prob. 1CCCh. 10.7 - Prob. 1PCh. 10.7 - Prob. 2PCh. 10.7 - Prob. 3PCh. 10.7 - Prob. 4PCh. 10.7 - Prob. 5PCh. 10.7 - Prob. 6PCh. 10.7 - Prob. 7PCh. 10.7 - Prob. 8PCh. 10.7 - Prob. 1VRVCCh. 10.7 - Prob. 2VRVCCh. 10.7 - Prob. 3VRVCCh. 10.7 - Prob. 4VRVCCh. 10.7 - Prob. 5VRVCCh. 10.7 - Prob. 6VRVCCh. 10.7 - Prob. 1ECh. 10.7 - Prob. 2ECh. 10.7 - Prob. 3ECh. 10.7 - Prob. 4ECh. 10.7 - Prob. 5ECh. 10.7 - Prob. 6ECh. 10.7 - Prob. 7ECh. 10.7 - Prob. 8ECh. 10.7 - Prob. 9ECh. 10.7 - Prob. 10ECh. 10.7 - Prob. 11ECh. 10.7 - Prob. 12ECh. 10.7 - Prob. 13ECh. 10.7 - Prob. 14ECh. 10.7 - Prob. 15ECh. 10.7 - Prob. 16ECh. 10.7 - Prob. 17ECh. 10.7 - Prob. 18ECh. 10.7 - Prob. 19ECh. 10.7 - Prob. 20ECh. 10.7 - Prob. 21ECh. 10.7 - Prob. 22ECh. 10.7 - Prob. 23ECh. 10.7 - Prob. 24ECh. 10.7 - Prob. 25ECh. 10.7 - Prob. 26ECh. 10.7 - Prob. 27ECh. 10.7 - Prob. 28ECh. 10.7 - Prob. 29ECh. 10.7 - Prob. 30ECh. 10.7 - Prob. 31ECh. 10.7 - Prob. 32ECh. 10.7 - Prob. 33ECh. 10.7 - Prob. 34ECh. 10.7 - Prob. 35ECh. 10.7 - Prob. 36ECh. 10.7 - Prob. 37ECh. 10.7 - Prob. 38ECh. 10.7 - Prob. 39ECh. 10.7 - Prob. 40ECh. 10.7 - Prob. 41ECh. 10.7 - Prob. 42ECh. 10.7 - Prob. 43ECh. 10.7 - Prob. 44ECh. 10.7 - Prob. 45ECh. 10.7 - Prob. 46ECh. 10.7 - Prob. 47ECh. 10.7 - Prob. 48ECh. 10.7 - Prob. 49ECh. 10.7 - Prob. 50ECh. 10.7 - Prob. 51ECh. 10.7 - Prob. 52ECh. 10.7 - Prob. 53ECh. 10.7 - Prob. 54ECh. 10.7 - Prob. 55ECh. 10.7 - Prob. 56ECh. 10.7 - Prob. 57ECh. 10.7 - Prob. 58ECh. 10.7 - Prob. 59ECh. 10.7 - Prob. 60ECh. 10.7 - Prob. 61ECh. 10.7 - Prob. 62ECh. 10.GA - Prob. 1GACh. 10.GA - Prob. 2GACh. 10.GA - Prob. 3GACh. 10.GA - Prob. 4GACh. 10.VC - Prob. 1VCCh. 10.VC - Prob. 2VCCh. 10.VC - Prob. 3VCCh. 10.VC - Prob. 4VCCh. 10.VC - Prob. 5VCCh. 10.VC - Prob. 6VCCh. 10.VC - Prob. 7VCCh. 10.VC - Prob. 8VCCh. 10.VC - Prob. 9VCCh. 10.VC - Prob. 10VCCh. 10.CR - Prob. 1CRCh. 10.CR - Prob. 2CRCh. 10.CR - Prob. 3CRCh. 10.CR - Prob. 4CRCh. 10.CR - Prob. 5CRCh. 10.CR - Prob. 6CRCh. 10.CR - Prob. 7CRCh. 10.CR - Prob. 8CRCh. 10.CR - Prob. 9CRCh. 10.CR - Prob. 10CRCh. 10.CR - Prob. 11CRCh. 10.CR - Prob. 12CRCh. 10.CR - Prob. 13CRCh. 10.CR - Prob. 14CRCh. 10.CR - Prob. 15CRCh. 10.CR - Prob. 16CRCh. 10.CR - Prob. 17CRCh. 10.CR - Prob. 18CRCh. 10.CR - Prob. 19CRCh. 10.CR - Prob. 20CRCh. 10.CR - Prob. 21CRCh. 10.CR - Prob. 22CRCh. 10.CR - Prob. 23CRCh. 10.CR - Prob. 24CRCh. 10.CR - Prob. 25CRCh. 10.CR - Prob. 26CRCh. 10.CR - Prob. 27CRCh. 10.CR - Prob. 28CRCh. 10.CR - Prob. 29CRCh. 10.CR - Prob. 30CRCh. 10.CR - Prob. 31CRCh. 10.CR - Prob. 32CRCh. 10.CR - Prob. 33CRCh. 10.CR - Prob. 34CRCh. 10.CR - Prob. 35CRCh. 10.CR - Prob. 36CRCh. 10.CR - Prob. 37CRCh. 10.CR - Prob. 38CRCh. 10.CR - Prob. 39CRCh. 10.CR - Prob. 40CRCh. 10.CR - Prob. 41CRCh. 10.CR - Prob. 42CRCh. 10.CR - Prob. 43CRCh. 10.CR - Prob. 44CRCh. 10.CR - Prob. 45CRCh. 10.CR - Prob. 46CRCh. 10.CR - Prob. 47CRCh. 10.CR - Prob. 48CRCh. 10.CR - Prob. 49CRCh. 10.CR - Prob. 50CRCh. 10.CR - Prob. 51CRCh. 10.CR - Prob. 52CRCh. 10.CR - Prob. 53CRCh. 10.CR - Prob. 54CRCh. 10.CR - Prob. 55CRCh. 10.CR - Prob. 56CRCh. 10.CR - Prob. 57CRCh. 10.CR - Prob. 58CRCh. 10.CR - Prob. 59CRCh. 10.CR - Prob. 60CRCh. 10.CR - Prob. 61CRCh. 10.CR - Prob. 62CRCh. 10.CR - Prob. 63CRCh. 10.CR - Prob. 64CRCh. 10.CR - Prob. 65CRCh. 10.CR - Prob. 66CRCh. 10.CR - Prob. 67CRCh. 10.CR - Prob. 68CRCh. 10.CR - Prob. 69CRCh. 10.CR - Prob. 70CRCh. 10.CR - Prob. 71CRCh. 10.CR - Prob. 72CRCh. 10.CR - Prob. 73CRCh. 10.CR - Prob. 74CRCh. 10.CR - Prob. 75CRCh. 10.CR - Prob. 76CRCh. 10.CR - Prob. 77CRCh. 10.CR - Prob. 78CRCh. 10.CR - Prob. 79CRCh. 10.CR - Prob. 80CRCh. 10.CR - Prob. 81CRCh. 10.CR - Prob. 82CRCh. 10.CR - Prob. 83CRCh. 10.CR - Prob. 84CRCh. 10.CR - Prob. 85CRCh. 10.CR - Prob. 86CRCh. 10.CR - Prob. 87CRCh. 10.CR - Prob. 88CRCh. 10.CR - Prob. 89CRCh. 10.CR - Prob. 90CRCh. 10.CR - Prob. 91CRCh. 10.CR - Prob. 92CRCh. 10.CR - Prob. 93CRCh. 10.CR - Prob. 94CRCh. 10.CR - Prob. 95CRCh. 10.CR - Prob. 96CRCh. 10.CR - Prob. 97CRCh. 10.CR - Prob. 98CRCh. 10.CR - Prob. 99CRCh. 10.CR - Prob. 100CRCh. 10.CR - Prob. 101CRCh. 10.CR - Prob. 102CRCh. 10.CR - Prob. 103CRCh. 10.CR - Prob. 104CRCh. 10.CR - Prob. 105CRCh. 10.CR - Prob. 106CRCh. 10.CR - Prob. 107CRCh. 10.CR - Prob. 108CRCh. 10.CR - Prob. 109CRCh. 10.CR - Prob. 110CRCh. 10.CR - Prob. 111CRCh. 10.CR - Prob. 112CRCh. 10.CR - Prob. 113CRCh. 10.CR - Prob. 114CRCh. 10.CR - Prob. 115CRCh. 10.CR - Prob. 116CRCh. 10.CR - Prob. 117CRCh. 10.CR - Prob. 118CRCh. 10.CR - Prob. 119CRCh. 10.CR - Prob. 120CRCh. 10.CR - Prob. 121CRCh. 10.CR - Prob. 122CRCh. 10.CR - Prob. 123CRCh. 10.CR - Prob. 124CRCh. 10.CR - Prob. 125CRCh. 10.CR - Prob. 126CRCh. 10.CR - Prob. 127CRCh. 10.CR - Prob. 128CRCh. 10.CR - Prob. 129CRCh. 10.CR - Prob. 130CRCh. 10.CR - Prob. 131CRCh. 10.CR - Prob. 132CRCh. 10.CR - Prob. 133CRCh. 10.CR - Prob. 134CRCh. 10.CR - Prob. 135CRCh. 10.CR - Prob. 136CRCh. 10.CR - Prob. 137CRCh. 10.CR - Prob. 138CRCh. 10.CR - Prob. 139CRCh. 10.CR - Prob. 140CRCh. 10.CR - Prob. 141CRCh. 10.CR - Prob. 142CRCh. 10.CT - Prob. 1CTCh. 10.CT - Prob. 2CTCh. 10.CT - Prob. 3CTCh. 10.CT - Prob. 4CTCh. 10.CT - Prob. 5CTCh. 10.CT - Prob. 6CTCh. 10.CT - Prob. 7CTCh. 10.CT - Prob. 8CTCh. 10.CT - Prob. 9CTCh. 10.CT - Prob. 10CTCh. 10.CT - Prob. 11CTCh. 10.CT - Prob. 12CTCh. 10.CT - Prob. 13CTCh. 10.CT - Prob. 14CTCh. 10.CT - Prob. 15CTCh. 10.CT - Prob. 16CTCh. 10.CT - Prob. 17CTCh. 10.CT - Prob. 18CTCh. 10.CT - Prob. 19CTCh. 10.CT - Prob. 20CTCh. 10.CT - Prob. 21CTCh. 10.CT - Prob. 22CTCh. 10.CT - Prob. 23CTCh. 10.CT - Prob. 24CTCh. 10.CT - Prob. 25CTCh. 10.CT - Prob. 26CTCh. 10.CT - Prob. 27CTCh. 10.CT - Prob. 28CTCh. 10.CT - Prob. 29CTCh. 10.CT - Prob. 30CTCh. 10.CT - Prob. 31CTCh. 10.CM - Prob. 1CMCh. 10.CM - Prob. 2CMCh. 10.CM - Prob. 3CMCh. 10.CM - Prob. 4CMCh. 10.CM - Prob. 5CMCh. 10.CM - Prob. 6CMCh. 10.CM - Prob. 7CMCh. 10.CM - Prob. 8CMCh. 10.CM - Prob. 9CMCh. 10.CM - Prob. 10CMCh. 10.CM - Prob. 11CMCh. 10.CM - Prob. 12CMCh. 10.CM - Prob. 13CMCh. 10.CM - Prob. 14CMCh. 10.CM - Prob. 15CMCh. 10.CM - Prob. 16CMCh. 10.CM - Prob. 17CMCh. 10.CM - Prob. 18CMCh. 10.CM - Prob. 19CMCh. 10.CM - Prob. 20CMCh. 10.CM - Prob. 21CMCh. 10.CM - Prob. 22CMCh. 10.CM - Prob. 23CMCh. 10.CM - Prob. 24CMCh. 10.CM - Prob. 25CMCh. 10.CM - Prob. 26CMCh. 10.CM - Prob. 27CMCh. 10.CM - Prob. 28CMCh. 10.CM - Prob. 29CMCh. 10.CM - Prob. 30CMCh. 10.CM - Prob. 31CMCh. 10.CM - Prob. 32CMCh. 10.CM - Prob. 33CMCh. 10.CM - Prob. 34CMCh. 10.CM - Prob. 35CMCh. 10.CM - Prob. 36CMCh. 10.CM - Prob. 37CMCh. 10.CM - Prob. 38CMCh. 10.CM - Prob. 39CMCh. 10.CM - Prob. 40CMCh. 10.CM - Prob. 41CMCh. 10.CM - Prob. 42CMCh. 10.CM - Prob. 43CMCh. 10.CM - Prob. 44CMCh. 10.CM - Prob. 45CMCh. 10.CM - Prob. 46CMCh. 10.CM - Prob. 47CMCh. 10.CM - Prob. 48CMCh. 10.CM - Prob. 49CMCh. 10.CM - Prob. 50CMCh. 10.CM - Prob. 51CMCh. 10.CM - Prob. 52CM
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