Developmental Mathematics (9th Edition)
9th Edition
ISBN: 9780321997173
Author: Marvin L. Bittinger, Judith A. Beecher
Publisher: PEARSON
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Chapter A, Problem 23DE
To determine
To fill: The blank in the statement, “"
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1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
-2
3
2) Given the following matrices A =
-1
0
1] an
and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of
the following sets and the cardinal number of each set.
a) W° and n(W)
b) (VUW) and n((V U W)')
c) VUWUX and n(V U W UX)
d) vnWnX and n(V WnX)
9) Use the Venn Diagram given below to determine the number elements in each of the following sets.
a) n(A).
b) n(A° UBC).
U
B
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Chapter A Solutions
Developmental Mathematics (9th Edition)
Ch. A - Use the unit below to measure the length of each...Ch. A - Prob. 2DECh. A - Prob. 3DECh. A - Prob. 4DECh. A - Prob. 5DECh. A - Prob. 6DECh. A - Prob. 7DECh. A - Prob. 8DECh. A - Prob. 9DECh. A - Prob. 10DE
Ch. A - Prob. 11DECh. A - Prob. 12DECh. A - Prob. 13DECh. A - Prob. 14DECh. A - Prob. 15DECh. A - Prob. 16DECh. A - Prob. 17DECh. A - Prob. 18DECh. A - Prob. 19DECh. A - Prob. 20DECh. A - Prob. 21DECh. A - Prob. 22DECh. A - Prob. 23DECh. A - Prob. 24DECh. A - Prob. 25DECh. A - Prob. 26DECh. A - Prob. 27DECh. A - Prob. 28DECh. A - Prob. 29DECh. A - Prob. 30DECh. A - Prob. 31DECh. A - Prob. 32DECh. A - Prob. 33DECh. A - Complete. Try to do this mentally using the...Ch. A - Prob. 35DECh. A - Prob. 36DECh. A - Prob. 37DECh. A - Prob. 38DECh. A - Prob. 39DECh. A - Prob. 40DECh. A - Prob. 1ESCh. A - Prob. 2ESCh. A - Prob. 3ESCh. A - Prob. 4ESCh. A - Prob. 5ESCh. A - Prob. 6ESCh. A - Prob. 7ESCh. A - Prob. 8ESCh. A - Prob. 9ESCh. A - Prob. 10ESCh. A - Prob. 11ESCh. A - Prob. 12ESCh. A - Prob. 13ESCh. A - Prob. 14ESCh. A - Prob. 15ESCh. A - Prob. 16ESCh. A - Prob. 17ESCh. A - Prob. 18ESCh. A - Prob. 19ESCh. A - Prob. 20ESCh. A - Prob. 21ESCh. A - Prob. 22ESCh. A - Prob. 23ESCh. A - Prob. 24ESCh. A - Prob. 25ESCh. A - Prob. 26ESCh. A - Prob. 27ESCh. A - Prob. 28ESCh. A - Prob. 29ESCh. A - Prob. 30ESCh. A - Prob. 31ESCh. A - Prob. 32ESCh. A - Prob. 33ESCh. A - Prob. 34ESCh. A - Prob. 35ESCh. A - Prob. 36ESCh. A - b Complete. Do as much as possible mentally. a....Ch. A - Prob. 38ESCh. A - Prob. 39ESCh. A - Prob. 40ESCh. A - Prob. 41ESCh. A - Prob. 42ESCh. A - Prob. 43ESCh. A - Prob. 44ESCh. A - Prob. 45ESCh. A - Prob. 46ESCh. A - Prob. 47ESCh. A - Prob. 48ESCh. A - Prob. 49ESCh. A - Prob. 50ESCh. A - Prob. 51ESCh. A - Prob. 52ESCh. A - Prob. 53ESCh. A - Prob. 54ESCh. A - Prob. 55ESCh. A - Prob. 56ESCh. A - Prob. 57ESCh. A - Prob. 58ESCh. A - Prob. 59ESCh. A - Prob. 60ESCh. A - Prob. 61ESCh. A - Prob. 62ESCh. A - Prob. 63ESCh. A - Prob. 64ESCh. A - Prob. 65ESCh. A - Prob. 66ESCh. A - Prob. 67ESCh. A - Prob. 68ESCh. A - Prob. 69ESCh. A - Prob. 70ESCh. A - Prob. 71ESCh. A - Prob. 72ESCh. A - Prob. 73ESCh. A - Prob. 74ESCh. A - Prob. 75ESCh. A - Prob. 76ESCh. A - Prob. 77ESCh. A - Prob. 78ESCh. A - Prob. 79ESCh. A - Prob. 80ESCh. A - Prob. 81ESCh. A - Prob. 82ESCh. A - Prob. 83ESCh. A - Prob. 84ESCh. A - Prob. 85ESCh. A - Prob. 86ESCh. A - Prob. 87ESCh. A - Prob. 88ESCh. A - Prob. 89ESCh. A - Prob. 90ESCh. A - Prob. 91ESCh. A - Prob. 92ESCh. A - Prob. 93ESCh. A - Prob. 94ESCh. A - Prob. 95ESCh. A - Prob. 96ESCh. A - Prob. 97ESCh. A - Prob. 98ESCh. A - Prob. 99ESCh. A - Prob. 100ESCh. A - Prob. 101ESCh. A - Prob. 102ESCh. A - Prob. 103ESCh. A - Prob. 104ESCh. A - Prob. 105ESCh. A - Prob. 106ESCh. A - Prob. 107ESCh. A - Prob. 108ESCh. A - Prob. 109ESCh. A - Prob. 110ESCh. A - Prob. 111ESCh. A - Prob. 112ESCh. A - Prob. 113ESCh. A - Prob. 114ESCh. A - Prob. 115ESCh. A - Prob. 116ES
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- 10) Find n(K) given that n(T) = 7,n(KT) = 5,n(KUT) = 13.arrow_forward7) Use the Venn Diagram below to determine the sets A, B, and U. A = B = U = Blue Orange white Yellow Black Pink Purple green Grey brown Uarrow_forward8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.arrow_forward
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- 3) What is the universal set that contains all possible integers from 1 to 8 inclusive? Choose one. a) A = {1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8} b) B={-1,0,1,2,3,4,5,6,7,8} c) C={1,2,3,4,5,6,7,8} d) D = {0,1,2,3,4,5,6,7,8}arrow_forwardA smallish urn contains 25 small plastic bunnies – 7 of which are pink and 18 of which are white. 10 bunnies are drawn from the urn at random with replacement, and X is the number of pink bunnies that are drawn. (a) P(X = 5) ≈ (b) P(X<6) ≈ The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a) The probability that the Grinch gets exactly 6 blue marbles is [ Select ] ["≈ 0.054", "≈ 0.043", "≈ 0.061"] . (b) The probability that the Grinch gets at least 7 blue marbles is [ Select ] ["≈ 0.922", "≈ 0.905", "≈ 0.893"] . (c) The probability that the Grinch gets between 8 and 12 blue marbles (inclusive) is [ Select ] ["≈ 0.801", "≈ 0.760", "≈ 0.786"] . The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a)…arrow_forwardUsing Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates).arrow_forward
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