EBK COLLEGE ALGEBRA WITH MODELING & VIS
6th Edition
ISBN: 8220103631242
Author: Rockswold
Publisher: Pearson Education (US)
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Question
Chapter R1, Problem 49E
To determine
the surface area and volume of a sphere.
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Check out a sample textbook solutionStudents have asked these similar questions
Let
2
A =
4
3
-4
0
1
(a) Show that v =
eigenvalue.
()
is an eigenvector of A and find the corresponding
(b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a)
may be useful.
(c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces.
(d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.
(c) Let
6
0 0
A =
-10 4 8
5 1 2
(i) Find the characteristic polynomial of A and factorise it.
(ii) Determine all eigenvalues of A and find bases for the corresponding
eigenspaces.
(iii) Is A diagonalisable? Give reasons for your answer.
most 2, and let
Let P2 denote the vector space of polynomials of degree at
D: P2➡ P2
be the transformation that sends a polynomial p(t) = at² + bt+c in P2 to its derivative
p'(t)
2at+b, that is,
D(p) = p'.
(a) Prove that D is a linear transformation.
(b) Find a basis for the kernel ker(D) of the linear transformation D and compute its
nullity.
(c) Find a basis for the image im(D) of the linear transformation D and compute its
rank.
(d) Verify that the Rank-Nullity Theorem holds for the linear transformation D.
(e) Find the matrix representation of D in the standard basis (1,t, t2) of P2.
Chapter R1 Solutions
EBK COLLEGE ALGEBRA WITH MODELING & VIS
Ch. R1 - Prob. 1ECh. R1 - Prob. 2ECh. R1 - Prob. 3ECh. R1 - Prob. 4ECh. R1 - Prob. 5ECh. R1 - Prob. 6ECh. R1 - Prob. 7ECh. R1 - Prob. 8ECh. R1 - Prob. 9ECh. R1 - Prob. 10E
Ch. R1 - Prob. 11ECh. R1 - Prob. 12ECh. R1 - Prob. 13ECh. R1 - Prob. 14ECh. R1 - Prob. 15ECh. R1 - Prob. 16ECh. R1 - Prob. 17ECh. R1 - Prob. 18ECh. R1 - Prob. 19ECh. R1 - Prob. 20ECh. R1 - Prob. 21ECh. R1 - Prob. 22ECh. R1 - Prob. 23ECh. R1 - Prob. 24ECh. R1 - Prob. 25ECh. R1 - Prob. 26ECh. R1 - Prob. 27ECh. R1 - Prob. 28ECh. R1 - Prob. 29ECh. R1 - Prob. 30ECh. R1 - Prob. 31ECh. R1 - Prob. 32ECh. R1 - Prob. 33ECh. R1 - Prob. 34ECh. R1 - Prob. 35ECh. R1 - Prob. 36ECh. R1 - Prob. 37ECh. R1 - Prob. 38ECh. R1 - Prob. 39ECh. R1 - Prob. 40ECh. R1 - Prob. 41ECh. R1 - Prob. 42ECh. R1 - Prob. 43ECh. R1 - Prob. 44ECh. R1 - Prob. 45ECh. R1 - Prob. 46ECh. R1 - Prob. 47ECh. R1 - Prob. 48ECh. R1 - Prob. 49ECh. R1 - Prob. 50ECh. R1 - Prob. 51ECh. R1 - Prob. 52ECh. R1 - Prob. 53ECh. R1 - Prob. 54ECh. R1 - Prob. 55ECh. R1 - Prob. 56ECh. R1 - Prob. 57ECh. R1 - Prob. 58ECh. R1 - Prob. 59ECh. R1 - Prob. 60ECh. R1 - Prob. 61ECh. R1 - Prob. 62ECh. R1 - Prob. 63ECh. R1 - Prob. 64E
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