15. Let T: P₂M22 be the linear transformation defined by p(0) p(1)] T(p) = - P(-1) let B be the standard basis for M22, and let B' = {1, x, x²}, B" = {1,1 + x, 1 + x2} be bases for P2. a. Find [T]B, B and [T]B,B". b. For the matrices obtained in part (a), find T(2 + 2x + x²) using the three-step procedure illustrated in Example 2. c. Check the results obtained in part (b) by computing T(2 + 2x + x²) directly.

15. Let T: P₂M22 be the linear transformation defined by p(0) p(1)] T(p) = - P(-1) let B be the standard basis for M22, and let B' = {1, x, x²}, B" = {1,1 + x, 1 + x2} be bases for P2. a. Find [T]B, B and [T]B,B". b. For the matrices obtained in part (a), find T(2 + 2x + x²) using the three-step procedure illustrated in Example 2. c. Check the results obtained in part (b) by computing T(2 + 2x + x²) directly.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...

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