Find the matrix [ T] C<--B of the linear transformation T : V ---> W with respect to the bases B and C of V and W, respectively. Verify by computing T(v) directly T: P1--->P1 defined by T ( a + bx) = b -ax, B= {l + x, 1 -x}, C = {l, x}, v = p (x) = 4 + 2x

Find the matrix [ T] C<--B of the linear transformation T : V ---> W with respect to the bases B and C of V and W, respectively. Verify by computing T(v) directly T: P1--->P1 defined by T ( a + bx) = b -ax, B= {l + x, 1 -x}, C = {l, x}, v = p (x) = 4 + 2x

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 23EQ

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Question

Find the matrix [ T] C<--B of the linear transformation T : V ---> W with respect to the bases B and C of V and W, respectively. Verify by computing T(v) directly T: P₁--->P₁ defined by T ( a + bx) = b -ax, B= {l + x, 1 -x}, C = {l, x}, v = p (x) = 4 + 2x

Expert Solution

Step 1

The given transformation is,

$T (a + b x) = b - a x$ , and The given bases are $B = \{1 + x, 1 - x\}, and C = \{1, x\}$ .

To Find: Matrix representation ${[T]}_{B \to C}$ for this transformation.

Also, we need to verify this matrix for the polynomial $p (x) = 4 + 2 x$ .

Step by step

Solved in 2 steps

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