Showing that two 4x4 matrices are similar

[hobochu]

Homework Statement

Given two 4x4 Matrices
A = [0 -1 1 1, -1 1 0 0, 0 0 -1 1, 0 0 0 0] B = [-0.5 -0.5 -0.5 -1.5, -0.5 1.5 0.5 -0.5, 0 0 -1 1, 0 0 0 0]

I need to show that these two matrices are similar.

Homework Equations

A = SBS^-1
which simplifies to AS = SB

The Attempt at a Solution

I understand that I need to find a non-singular invertible matrix S that satisfies the equation: AS = SB, but I have spent many hours trying to find out how to find this matrix for a 4x4 matrix. In the text and in many of the online help pages, there are only examples of 2x2 matrices that have a very obvious matrix. I have not learned eigenvalues or eigenvectors yet, and do not wish to use them unless there really is no other way to show similarity.

Thanks for any responses, and I appreciate any help on this problem.

 

[radou]

It's a matrix equation. Name the elements of the matrix S (i.e. sij), multiply the matrices in order to obtain a system of equations, and see what happens.

 

[lanedance]

just carring on from radou, S is not unique, if S is a solution, then so is 2S, so you just need to demonstrate any matrix that works