Solve Eigenvector Problem: Find Eigenvalues & Eigenvectors

[geft]

Homework Statement

Find the eigenvalues and eigenvectors of \left( \begin{array}{ccc} 2 & 0 & 0 \\ 0 & 3 & 4 \\ 1 & 1 & 0 \end{array} \right)

Homework Equations

p(\lambda) = det(A - \lambda I) = 0

The Attempt at a Solution

A - \lambda I = \left( \begin{array}{ccc} 2-\lambda & 0 & 0 \\ 0 & 3-\lambda & 4 \\ 1 & 1 & 0 \end{array} \right)

det(A - \lambda I) = (2 - \lambda)(-4) + 1 = 0

-8 + 4 \lambda + 1 = 0

4\lambda = 7

\lambda = \frac{4}{7}

A - \lambda I = \left( \begin{array}{ccc} \frac{1}{4} & 0 & 0 \\ 0 & \frac{5}{7} & 4 \\ 1 & 1 & 0 \end{array} \right)

\frac{1}{4}x_1 = 0

\frac{5}{4}x_2 + 4x_3 = 0

Eigenvector = \left( \begin{array}{ccc} 0 \\ 0 \\ 0 \end{array} \right)

 

[Mark44]

This should be in the Calculus and Beyond section.

For your formatting problems, use [ tex ] and [ /tex ] tags (without the extra spaces I put in, instead of the inline LaTeX tags, [ itex ], you used.

 

[geft]

Thanks. Should I repost this in the other section?

 

[Pengwuino]

As for the problem, in your A-\lambda I matrix, you still have a -\lambda in the 3rd row, 3rd column entry. It isn't simply 0.

 

[geft]

As for the problem, in your A-\lambda I matrix, you still have a -\lambda in the 3rd row, 3rd column entry. It isn't simply 0.

Oh, you're right. Thanks!