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Let T: P3 → P3 be the linear transformation given by the formula T(f) = f'- f, for any fe P3. (a) With the ordered basis B = {1,1,12) of P2, write down [T]B. For at least one column, explain how you got that column. (b) The matrix you wrote in part a has at least one real eigenvalue. Find a corresponding eigenvector. (c) Determine whether your matrix from part a is, or is not, diagonalizable. Justify your response. (d) Determine whether your matrix from part a is, or is not, invertible. Justify your response.

Let T: P3 → P3 be the linear transformation given by the formula T(f) = f'- f, for any fe P3. (a) With the ordered basis B = {1,1,12) of P2, write down [T]B. For at least one column, explain how you got that column. (b) The matrix you wrote in part a has at least one real eigenvalue. Find a corresponding eigenvector. (c) Determine whether your matrix from part a is, or is not, diagonalizable. Justify your response. (d) Determine whether your matrix from part a is, or is not, invertible. Justify your response.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let T: P3 fe P3. →→ P3 be the lincar transformation given by the formula T(ƒ) = f' – f, for any (a) With the ordered basis B = {1,1,12} of P2, write down [7]B. For at least one column, explain how you got that column. (b) The matrix you wrote in part a has at least one real eigenvalue. Find a corresponding eigenvector. (c) Determine whether your matrix from part a is, or is not, diagonalizable. Justify your response. (d) Determine whether your matrix from part a is, or is not, invertible. Justify your response.
Transcribed Image Text:Let T: P3 fe P3. →→ P3 be the lincar transformation given by the formula T(ƒ) = f' – f, for any (a) With the ordered basis B = {1,1,12} of P2, write down [7]B. For at least one column, explain how you got that column. (b) The matrix you wrote in part a has at least one real eigenvalue. Find a corresponding eigenvector. (c) Determine whether your matrix from part a is, or is not, diagonalizable. Justify your response. (d) Determine whether your matrix from part a is, or is not, invertible. Justify your response.
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