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## Homework Statement

Find the eigenvalues and eigenvectors of the matrix A = [2, 1; 8, 4]

## Homework Equations

det(A - lambda I) = 0

## The Attempt at a Solution

After expanding using the formula I have the equation (2 - [itex]\lambda[/itex])(4 - [itex]\lambda[/itex]) - 8

Which gives [itex]\lambda[/itex] = 0, 6 (Should I be worried that I got a zero in my answer?)

Then substituting the values for lambda back into the problem and using (A - [itex]\lambda[/itex]I)v = 0

For [itex]\lambda[/itex] = 6

[-4, 1; 8, -2] * [a; b] = [0; 0] and I get the eigenvector a[1; 4] from (-4a + b = 0)

For [itex]\lambda[/itex] = 0

[2, 1; 8, 4] * [a; b] = [0; 0] I get a second eigenvector of a[1; -2] from (2a + b = 0)

Did I get the right eigenvalues and corresponding eigenvectors?