- #1
misterau
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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)
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