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find matrix A given eigenvector and eigenvalue.?
Given that the matrix A has eigenvalues L1 = 8 with corresponding eigenvector v1 =(1,-3) L2=4 with corresponding eigenvector v2 =(1,-3), find A
typo v2 is (-1,4)
1 Answer
- HosamLv 68 years agoFavorite Answer
AP = PD, where P is the matrix of eigenvectors, and D is a diagonal matrix of the eigenvalues
v1 = (1, -3), and v2 = (1, 3), so
P = [v1 , v2 ] = [ 1, 1; -3, 3 ]
| P | = 6, and therefore P^-1 = 1/6 [3, -1; 3, 1]
A = P D P^-1 = 1/6 [1, 1; -3, 3] [8, 0; 0, 4] [3, -1; 3, 1]
= 1/6 [8, 4; -24, 12] [3, -1; 3, 1] = 1/6 [36, -4; -36, 36] = [6, -2/3; -6, 6]
