Prealgebra
8th Edition
ISBN: 9780134707648
Author: Martin-Gay, K. Elayn
Publisher: Pearson,
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Textbook Question
Chapter C, Problem 6E
Objective A Write each number in scientific notation. See Example 1.
0.00194
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(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.
(c) Let
A =
-1 3
-4 12
3
3
-9
(i) Find bases for row(A), col(A) and N(A).
(ii) Determine the rank and nullity of A, and verify that the Rank-Nullity
Theorem holds for the above matrix A.
Chapter C Solutions
Prealgebra
Ch. C - Write each number in scientific notation. a....Ch. C - Prob. 2PCh. C - Prob. 3PCh. C - Objective A Write each number in scientific...Ch. C - Objective A Write each number in scientific...Ch. C - Objective A Write each number in scientific...Ch. C - Objective A Write each number in scientific...Ch. C - Objective A Write each number in scientific...Ch. C - Objective A Write each number in scientific...Ch. C - Objective A Write each number in scientific...
Ch. C - Objective A Write each number in scientific...Ch. C - Prob. 9ECh. C - Objective A Write each number in scientific...Ch. C - Objective B Write each number in standard form....Ch. C - Objective B Write each number in standard form....Ch. C - Objective B Write each number in standard form....Ch. C - Objective B Write each number in standard form....Ch. C - Objective B Write each number in standard form....Ch. C - Prob. 16ECh. C - Objective B Write each number in standard form....Ch. C - Objective B Write each number in standard form....Ch. C - Objectives A B Mixed Practice See Examples 1 and...Ch. C - Objectives A B Mixed Practice See Examples 1 and...Ch. C - Objectives A B Mixed Practice See Examples 1 and...Ch. C - Objectives A B Mixed Practice See Examples 1 and...Ch. C - Objectives A B Mixed Practice See Examples 1 and...Ch. C - Objectives A B Mixed Practice See Examples 1 and...Ch. C - Objectives C Evaluate each expression using...Ch. C - Objectives C Evaluate each expression using...Ch. C - Objectives C Evaluate each expression using...Ch. C - Objectives C Evaluate each expression using...Ch. C - Objectives C Evaluate each expression using...Ch. C - Objectives C Evaluate each expression using...Ch. C - Objectives C Evaluate each expression using...Ch. C - Objectives C Evaluate each expression using...Ch. C - Objectives C Evaluate each expression using...Ch. C - Objectives C Evaluate each expression using...
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