(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

det(A - lambda I) = 0

3. 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?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Finding eigenvalues and eigenvectors of a matrix A

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