Originally Posted by
daklutz Was just wondering if I did this problem correctly
Diagonalize the matrix B
3 0 0
1 2 0
1 −1 4
That is, find matrices P and D so that D is diagonal
and P(inverse)BP = D.
So to find P, I found the eigenvalues, 2,3,4,
then fond the eigenvectors by plugging in 2,3,4 respectively, so
when eigenvalue is 2,
1 0 0
1 0 0
1 -1 2
which gave me the eigen vector [0 .5 1]
when eigenvalue is 3,
0 0 0
1 -1 0
1 -1 1
which gave me the eigen vector [1 1 0]
when eigenvalue is 4,
-1 0 0
1 -2 0
1 -1 2
which gave me the eigen vector [0 0 1]
so P =
0 1 0
.5 1 0
1 0 1
Then P inverse has to be
-2 2 0
1 0 0
2 -2 1
and so D =
2 0 0
0 3 0
0 0 4
Did I do this problem correctly?