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2. The matrix of a linear transformation T is given by 8 (a) A basis of R² is given by B = {(3,4), (-2,-3)}. You are given the B-matrix for the transformation Tis (b) (c) A: = [T] B = M = what is w? B -5 3 can be written as M = P-¹AP. What is From lecture, we know the B-matrix the matrix P (write out the matrix)? If [w]B = [3], By inspection, determine [(-5, -7)]B. -2 1

2. The matrix of a linear transformation T is given by 8 (a) A basis of R² is given by B = {(3,4), (-2,-3)}. You are given the B-matrix for the transformation Tis (b) (c) A: = [T] B = M = what is w? B -5 3 can be written as M = P-¹AP. What is From lecture, we know the B-matrix the matrix P (write out the matrix)? If [w]B = [3], By inspection, determine [(-5, -7)]B. -2 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. The matrix of a linear transformation T is given by ^-1 A = A basis of R² is given by B = {(3,4), (-2,-3)}. You are given the B-matrix for the transformation Tis [T]B = M = (b) (c) (d) 13] (a) From lecture, we know the B-matrix can be written as M = P-¹AP. What is the matrix P (write out the matrix)? If [w])s = [3] By inspection, determine [(-5, -7)]B. Use the appropriate parts of the problem to help you determine how to write T(-5, -7) as a linear combination of the basis vectors in B. Write out the linear combination. Computing T(-5, -7) explicitly is optional, but can help for partial credit and to check if your answer makes sense. what is w? -2 1 -5 3
Transcribed Image Text:2. The matrix of a linear transformation T is given by ^-1 A = A basis of R² is given by B = {(3,4), (-2,-3)}. You are given the B-matrix for the transformation Tis [T]B = M = (b) (c) (d) 13] (a) From lecture, we know the B-matrix can be written as M = P-¹AP. What is the matrix P (write out the matrix)? If [w])s = [3] By inspection, determine [(-5, -7)]B. Use the appropriate parts of the problem to help you determine how to write T(-5, -7) as a linear combination of the basis vectors in B. Write out the linear combination. Computing T(-5, -7) explicitly is optional, but can help for partial credit and to check if your answer makes sense. what is w? -2 1 -5 3
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