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14. The matrix A is the same as above. (d) Diagonalize A, if possible. In other words, find a diagonal D and an invertible P such that A = PDP-1. If A is not diagonalizable, explain why not. Show by direct calculation that A2 = A. (e) (f) Give a geometric explanation why A² = A, using the fact that A is the standard matrix of the projection T.

14. The matrix A is the same as above. (d) Diagonalize A, if possible. In other words, find a diagonal D and an invertible P such that A = PDP-1. If A is not diagonalizable, explain why not. Show by direct calculation that A2 = A. (e) (f) Give a geometric explanation why A² = A, using the fact that A is the standard matrix of the projection T.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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14. The matrix A is the same as above. (d) Diagonalize A, if possible. In other words, find a diagonal D and an invertible P such that A = PDP-1. If A is not diagonalizable, explain why not. Show by direct calculation that A² = A. (e) (f) Give a geometric explanation why A² = A, using the fact that A is the standard matrix of the projection T.
Transcribed Image Text:14. The matrix A is the same as above. (d) Diagonalize A, if possible. In other words, find a diagonal D and an invertible P such that A = PDP-1. If A is not diagonalizable, explain why not. Show by direct calculation that A² = A. (e) (f) Give a geometric explanation why A² = A, using the fact that A is the standard matrix of the projection T.
A = 8 -25 -2 -27 -4 5 * * -2 -4
Transcribed Image Text:A = 8 -25 -2 -27 -4 5 * * -2 -4
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