- #1

- 20

- 0

## Homework Statement

A =

-10 6 3

-26 16 8

16 -10 -5

B =

0 -6 -16

0 17 45

0 -6 -16

(a) Show that 0, -1 and 2 are eigenvalues both of A and of B .

(b) Find invertible matrices P and Q so that (P^-1)*(A)*(P) = (Q^-1)*(B)*(Q)=

0 0 0

0 -1 0

0 0 2

(c) Find an invertible matrix R for which (R^-1)*(A)*(R) = B

## Homework Equations

## The Attempt at a Solution

I was able to do Q1 and Q2 but not Q3.

For Q2:

P =

0 1 1

-1 2 3

2 -1 -2

Q =

1 2 1

0 -5 -3

2 2 1

Not really sure about Q3, since matrix B is not in the form I am used too.

edit: I thought about it.

using, (P^-1)*(A)*(P) = (Q^-1)*(B)*(Q)

(Q)*(P^-1)*(A)*(P)*(Q^-1) = (Q)*(Q^-1)*(B)*(Q)*(Q^-1)

(Q)*(P^-1)*(A)*(P)*(Q^-1) = (B)

R = (P)*(Q^-1)

Last edited: