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

  • #1
672
0

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?
 

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Answers and Replies

  • #2
938
9
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 [itex] A = S \Lambda S^{-1} [/itex] with 1 a couple of times, only write it as [itex] 1 = S_1 S_1^{-1} [/itex].
 
  • #3
672
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Yak they gave me uppercase lamda and S what I am confused on is how to find S1.
 
  • #4
DryRun
Gold Member
838
4
You should multiply both sides of equation [itex] A = S \Lambda S^{-1} [/itex] with 1 a couple of times, only write it as [itex] 1 = S_1 S_1^{-1} [/itex].

As suggested by clamtrox, just multiply both sides by the 3x3 unit vector.
 
  • #5
672
0
I am confused if I do that I just get the same matrix again and I cant calculate A so what do I do?
 
  • #6
938
9
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.
 
  • #7
672
0
ok I think I got it
 

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