Orthogonally diagonalize the matrix, giving an orthogonal matrix p and a diagonal matrix d. to save time, the eigenvalues are -14 and -5.
-9 -4 21 -4 -9 2 2 2 -6

Step-by-step explanation:

It is a result that a matrix is orthogonally diagonalizable if and only if is a symmetric matrix.  According with the data you provided the matrix should be

We know that its eigenvalues are , where has multiplicity two.

So if we calculate the corresponding eigenspaces for each eigenvalue we have

,.

With this in mind we can form the matrices that diagonalizes the matrix so.

and

Observe that the rows of are the eigenvectors corresponding to the eigen values.

Now you only need to normalize each row of dividing by its norm, as a row vector.

The matrix you have to obtain is the matrix shown below

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent