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Eigenvalue and eigenvector

For a quare matrix , the eigenvalue and eigenvector have these relationships,

What is I?

is an identity matrix, meaning it has nothing but 0's with a diagonal of 1's, equivalent to the size of A. For a 2x2 matrix A, we would have,

For a 3x3 matrix A, we would have,

A 2x2 matrix A

So if we know this,

Then we get this quadratic equation,

Remember the quadratic formula to find ,