Explaining and Solving Matrix Inverses - Homework Question | Charismaztex

[Charismaztex]

Homework Statement

a)Suppose we know that M^2+M-6I=0 where M is a square matrix. Explain why inverse of M exists, and find inverse of M in terms of M.

b) For A= 0 1 0 calculate A^22. Does the inverse of A exist?
0 0 1
1 0 0

c) Let u be any unit vector in R^n and B=I-uu^T prove that
i) B=B^T
ii) B^2=B

Homework Equations

The Attempt at a Solution

For a) I just can't get the subject to be M inverse.

b) I've got A^2 and A^3...

c) I'm a little lost here...

I don't seem to have much handle on this topic so
any help is greatly appreciated,

Charismaztex

 

[VeeEight]

For the first problem, try rearranging the formula. Bring the '6I' term to the other side and try rearranging the remaining terms. You want something of the form M(something) = I

 

[FieldDuck]

a)I can't tell you what you're missing if I don't see how you're solving the problem so show me your work and then we can work together to find out that aspect you're not seeing.

b)You may have seen this equation before
A = PDP^-1, where P is invertible and D is diagonal, then we can say
A^k = PD^kP^1
so you might want to consider that and see what happens.

c)Once again take a leap of faith and show me what you're doing. You may be completely wrong, but this helps more than me just telling you what needs to happen.