Explanation Given: T : M 2 ( ℝ ) → ℝ 2 is, T ( A ) = ( t r ( A ) , t r ( A ) ) B = { E 11 , E 12 , E 21 , E 22 } ; C = { ( 1 , 0 ) ( 0 , 1 ) } ... ( 1 ) B = { [ − 1 − 2 − 2 − 3 ] , [ 1 1 2 2 ] , [ 0 − 3 2 − 2 ] , [ 0 4 1 0 ] } ; C = { ( 1 , 0 ) ( 0 , 1 ) } Approach: The matrix E i j is matrix with 1 in its ( i , j ) position and zeros in all other positions. So the, matrix T ( 1 ) is given by, T ( E 11 ) = [ 1 0 0 0 ] Calculation: Substitute 1 for a , 0 and for b , in equation ( 1 ) . T 2 T 1 = ( 0 , 0 ) Equate and compare ( 0 , 0 ) with a 1 ( 1 , 0 ) + a 2 ( 0 , 1 ) To determine (b) To verify: The theorem 6.5.7 by comparing part ( a ) with the product matrices in problem 5 and 10 . To determine (c) To find: The value of ( T 2 T 1 ) ( − 3 + 8 x ) and verify the answer.

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

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Question

Chapter 6.5, Problem 17P

To determine

(a)

To find:

The matrix representation T2T1 relative to the standard bases.

To determine

(b)

To verify:

The theorem 6.5.7 by comparing part (a) with the product matrices in problem 5 and 10.

To determine

(c)

To find:

The value of (T2T1)(−3+8x) and verify the answer.

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Chapter 6.5, Problem 16P

Chapter 6.5, Problem 18P

Chapter 6 Solutions

Differential Equations and Linear Algebra (4th Edition)

Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - True-False Review For Questions a-f, decide if the...Ch. 6.1 - For problem 1-8, verify directly from Definition...Ch. 6.1 - For problems 1-8, verify directly from Definition...Ch. 6.1 - For problem 1-8, verify directly from Definition...Ch. 6.1 - For problem 1-8, verify directly from Definition...

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(a) To find: The matrix representation T 2 T 1 relative to the standard bases.

Solution Summary: The author explains that the matrix E_ij is a matrix with 1 in its position and zeros in all other positions.

Videos

(a)

To find:

The matrix representation T2T1 relative to the standard bases.

(b)

To verify:

The theorem 6.5.7 by comparing part (a) with the product matrices in problem 5 and 10.

(c)

To find:

The value of (T2T1)(−3+8x) and verify the answer.

Want to see the full answer?

Chapter 6 Solutions

(a) To find: The matrix representation T 2 T 1 relative to the standard bases.

Solution Summary: The author explains that the matrix E_ij is a matrix with 1 in its position and zeros in all other positions.

Videos

(a) To find: The matrix representation T2T1 relative to the standard bases.

(b) To verify: The theorem 6.5.7 by comparing part (a) with the product matrices in problem 5 and 10.

(c) To find: The value of (T2T1)(−3+8x) and verify the answer.

Want to see the full answer?

Chapter 6 Solutions

(a)

To find:

The matrix representation T2T1 relative to the standard bases.

(b)

To verify:

The theorem 6.5.7 by comparing part (a) with the product matrices in problem 5 and 10.

(c)

To find:

The value of (T2T1)(−3+8x) and verify the answer.