Suppose A is the matrix.
A =
7 4 16
2 5 8
-2 -2 -5
Find the eigenvalues of A and find an invertible matrix P such that
(P^-1)AP is a diagonal matrix. Write down an expression for the matrix A^7 and find A^7.
matrix
2008-04-17 3:31 pm
回答 (2)
2008-04-18 8:30 am
✔ 最佳答案
有一樣既eigenvalue唔代表搵唔倒個P既.....ANSWER在此:
http://i32.photobucket.com/albums/d50/pzsing/matrixq.jpg
2008-04-17 5:58 pm
Finding eigenvalues:
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Apr08/Crazymat1.jpg
Since 2 of the eigenvalues have the same value, the matrix P will NOT be intervible since it will have 2 same columes, implying that its determinant will be zero.
Also A7 is found by computation:
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Apr08/Crazymat2.jpg
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Apr08/Crazymat1.jpg
Since 2 of the eigenvalues have the same value, the matrix P will NOT be intervible since it will have 2 same columes, implying that its determinant will be zero.
Also A7 is found by computation:
圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Apr08/Crazymat2.jpg
參考: My Maths knowledge
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