What is the radius of the tall second cylinder with an 8.5" circumference?
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Answer:
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
