Problem:
Working With Matrices
Question: Any matrix B which is formed by the eigen vectors of a matrix A reduces the given matrix A to the diagonal form by the transformation (inverse of B)AB.
i.e., (inverse of B)AB = diagonal matrix
The eigen vectors of the matrix
A = [ 9 -1 9]
[ 3 -1 3]
[-7 1 -7]
are a [ 1] , b [ 4] and c [ 1]
[ 0] [ 1] [ 1].
[-1] [-3] [-1]
Writing the eigen vectors [1 ] , [ 1] as three columns of a matrix, we get a matrix.
[0 ] [ 1]
[-1] [-1]
B= [ 1 4 1]
[ 0 1 1]
[-1 -3 -1]
Show that the matrix B reduces the given matrix A to the diagonal form by the transformation B-1 i.e., B-1 AB = diagonal matrix.