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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 =(-1,4), find A
1 Answer
- HosamLv 68 years ago
A P = P D
i.e. A = P D P^-1
where P is the matrix of eigenvectors, and D is the diagonal matrix of eigenvalues.
D = [ 8, 0; 0, 4 ]
P = [1, -1; -3, 4 ]
All we have to do is find P^-1.
| P | = 1, So P^-1 = [ 4, 1; 3, 1 ]
Finally A = P D P^-1 = [1, -1; -3, 4] [ 8, 0; 0, 4] [4, 1; 3, 1]
= [8, -4; -24, 16] [4, 1; 3, 1]
= [20, 4; -48, -8]
