Find a matrix S1 that satisfies A= S(uppercase lamda)S^(-1)

[DODGEVIPER13]

Homework Statement

A matrix S and a matrix A are given. Let A = S(uppercase lamda)S^-1, but do not calculate A. Find different S₁ and (Uppercase lamda)₁ such that the same A satisfies A = S₁(Uppercase lamda)₁S₁^-1

Homework Equations

The Attempt at a Solution

I have given the original matrices and my work on my attachment so see that for my work. What I want to know is what exactly is S₁ and (Uppercase lamda)₁ and how do I solve for them?

 

[clamtrox]

Your problem description doesn't make sense. I'm guessing you're given S and Lambda, not S and A.

You should multiply both sides of equation A = S \Lambda S^{-1} with 1 a couple of times, only write it as 1 = S_1 S_1^{-1}.

 

[DODGEVIPER13]

Yak they gave me uppercase lamda and S what I am confused on is how to find S₁.

 

[DryRun]

You should multiply both sides of equation A = S \Lambda S^{-1} with 1 a couple of times, only write it as 1 = S_1 S_1^{-1}.

As suggested by clamtrox, just multiply both sides by the 3x3 unit vector.

 

[DODGEVIPER13]

I am confused if I do that I just get the same matrix again and I can't calculate A so what do I do?

 

[clamtrox]

Of course you get the same matrix, that's the entire point. You want it to remain equal to A, but you want to write it in a different way.

 

[DODGEVIPER13]

ok I think I got it