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fuzzyorama
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Eigenvalues & Eigenvectors !SOLVED!
Find the eigenvalues and eigenvectors of matrix
[tex] A = \left( \begin{array}{cc} 2 & 2 \\ 3 & 1 \end{array} \right) [/tex]
[tex] Ax = \lambda x [/tex]
Solving
[tex] \left\vert \begin{array}{cc} 2 - \lambda & 2 \\ 3 & 1 - \lambda \end{array} \right\vert [/tex]
I get the eigenvalues [tex] \lambda = -1, 4[/tex]
When [tex] \lambda = 4[/tex]
[tex] \left( \begin{array}{cc} -2 & 2 \\ 3 & -2 \end{array} \right)\left( \begin{array}{c} x \\ y \end{array} \right) = 4\left( \begin{array}{c} x \\ y \end{array} \right) [/tex]
Then I get these equations [tex] -2x + 2y = 4x \mbox{~and~} 3x -3y = 4y [/tex]
From the first equation, [tex] y = 3x [/tex]. So is
[tex] x\left( \begin{array}{c} 4 \\ 12 \end{array} \right) [/tex] the eigenvector?
Homework Statement
Find the eigenvalues and eigenvectors of matrix
[tex] A = \left( \begin{array}{cc} 2 & 2 \\ 3 & 1 \end{array} \right) [/tex]
Homework Equations
[tex] Ax = \lambda x [/tex]
The Attempt at a Solution
Solving
[tex] \left\vert \begin{array}{cc} 2 - \lambda & 2 \\ 3 & 1 - \lambda \end{array} \right\vert [/tex]
I get the eigenvalues [tex] \lambda = -1, 4[/tex]
When [tex] \lambda = 4[/tex]
[tex] \left( \begin{array}{cc} -2 & 2 \\ 3 & -2 \end{array} \right)\left( \begin{array}{c} x \\ y \end{array} \right) = 4\left( \begin{array}{c} x \\ y \end{array} \right) [/tex]
Then I get these equations [tex] -2x + 2y = 4x \mbox{~and~} 3x -3y = 4y [/tex]
From the first equation, [tex] y = 3x [/tex]. So is
[tex] x\left( \begin{array}{c} 4 \\ 12 \end{array} \right) [/tex] the eigenvector?
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