Consider the transformation T:R? → R² given by [2x1 + 3x2] T(xie1 + x2e2) [4x1 – 5x2] 1. Verify that T is a linear transformation. 2. Compute the matrix of T relative to [27 E = {e1, e2} is the standard basis of R? and B = {b1 = b2 = |} 3. Is the transformation T diagonalizable? Why or why not? Justify your answer.

Consider the transformation T:R? → R² given by [2x1 + 3x2] T(xie1 + x2e2) [4x1 – 5x2] 1. Verify that T is a linear transformation. 2. Compute the matrix of T relative to [27 E = {e1, e2} is the standard basis of R? and B = {b1 = b2 = |} 3. Is the transformation T diagonalizable? Why or why not? Justify your answer.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Consider the transformation T:R² → R² given by
[2x1 + 3x2
T(x1e1 + c2e2) :
[4x1 – 5x2]
1. Verify that T is a linear transformation.
2. Compute the matrix of T relative to
[27
E = {e1, e2} is the standard basis of R? and B =
}
{b%3D
[2]
b2 =
3. Is the transformation T diagonalizable? Why or why not? Justify your answer.

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