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

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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,

Ta+bx=b-ax, and The given bases are B=1+x,1-x, and C=1,x.

To Find: Matrix representation TBC for this transformation.

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

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