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
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 17CM
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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,
, and The given bases are .
To Find: Matrix representation for this transformation.
Also, we need to verify this matrix for the polynomial .
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