How do I do

If A = , write A^2 in the form pA+qI where p and q are scalars?

How do I convert a square matrix to _A+_I?

Really need help, thank you so so much!

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- January 18th 2013, 08:18 AMTutuMatrices!
How do I do

If A = , write A^2 in the form pA+qI where p and q are scalars?

How do I convert a square matrix to _A+_I?

Really need help, thank you so so much! - January 18th 2013, 08:24 AMa tutorRe: Matrices!
- January 18th 2013, 08:41 AMHallsofIvyRe: Matrices!
I see no reason not to just

**do**this by straightforward calculation.

Since the problem asks about , the obvious first thing to do is to square A!

I presume you know that I is the identity matrix: so that, for any q, and then and that must be equal to .

That is, we have the four equations, 5- q= 3p, 4= 2p, -4= -2p, and -3- q= -p. Solve those equations for p and q.