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?