Hello

My daughter is doing a college assignment and I managed to help her with the majority of the question but cannot figure out the last part.

I have the characteristic equation and have made that a cubic but unsure on the M^-1 part

Thanks

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- Apr 11th 2012, 12:19 AMJane1947Help with question on matrices
Hello

My daughter is doing a college assignment and I managed to help her with the majority of the question but cannot figure out the last part.

I have the characteristic equation and have made that a cubic but unsure on the M^-1 part

Thanks - Apr 11th 2012, 01:22 AMDevenoRe: Help with question on matrices
ok, this is what i have, but you may want to check my arithmetic, because i DO make mistakes:

the Cayley-Hamilton theorem tells us M satisfies its own characteristic equation, which is .

therefore: , or put another way:

.

the trouble is now how to express in terms of . to accomplish that, we write:

, so that evidently:

, or:

, and re-arranging:

.

substituting back in our original equation:

, obtaining:

p = 23, q = -18, r = -40. - Apr 11th 2012, 05:23 AMJane1947Re: Help with question on matrices
Thanks very much for the time and effort you have put into this. I appreciate the answer and shall sit down with a pencil and try and explain it to her!