Intermediate Algebra
10th Edition
ISBN: 9781305191495
Author: Jerome E. Kaufmann; Karen L. Schwitters
Publisher: Cengage Learning US
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Chapter A, Problem 2PE
To determine
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Students 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 A Solutions
Intermediate Algebra
Ch. A - For Problems 1-6, Use Pascals triangle to help...Ch. A - Prob. 2PECh. A - For Problems 1-6, Use Pascals triangle to help...Ch. A - For Problems 1-6, Use Pascals triangle to help...Ch. A - Prob. 5PECh. A - Prob. 6PECh. A - Prob. 7PECh. A - Prob. 8PECh. A - Prob. 9PECh. A - Prob. 10PE
Ch. A - Prob. 11PECh. A - Prob. 12PECh. A - Prob. 13PECh. A - Prob. 14PECh. A - Prob. 15PECh. A - Prob. 16PECh. A - Prob. 17PECh. A - Prob. 18PECh. A - Prob. 19PECh. A - Prob. 20PECh. A - Prob. 21PECh. A - Prob. 22PECh. A - Prob. 23PECh. A - Prob. 24PECh. A - Prob. 25PECh. A - Prob. 26PECh. A - Prob. 27PECh. A - Prob. 28PECh. A - Prob. 29PECh. A - Prob. 30PECh. A - How would you explain binomial expansions to an...Ch. A - Prob. 32PE
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