eigenvalues and eigenvectors for the given matrix

[luckyc1423]

Find the eigenvalues and corresponding eigenvectors for the matrix

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[galactus]

Find your characteristic polynomial:

\(\displaystyle \L\\det({\lambda}I-A)\)

\(\displaystyle \text{I is the 2 by 2 identity matrix and\\A is your matrix}\)

\(\displaystyle \L\\det({\lambda}\begin{bmatrix}1&0\\0&1\end{bmatrix}-\begin{bmatrix}1&1\\4&1\end{bmatrix})\)

The roots of your charpoly will give you the eigenvalues.


Remember, \(\displaystyle \begin{bmatrix}x_{1}\\x_{2}\end{bmatrix}\)

is an eigenvector iff x is a nontrivial solution of \(\displaystyle ({\lambda}I-A)x=0\)

 

[pka]

Find the eigenvalues and corresponding eigenvectors for the matrix . . .[ 1 1 ]
. . .[ 4 1 ]

Lucky, still remember it is all about definitions, definitions, definitions.

 

[luckyc1423]

I appreciate everyones help, I am taking a summer class in linear algebra and my professor does a very poor job of explaining everything! So I post examples on here to see how you guys do it, then I can pretty much figure every other problem out by these examples

 

[daon]

I appreciate everyones help, I am taking a summer class in linear algebra and my professor does a very poor job of explaining everything! So I post examples on here to see how you guys do it, then I can pretty much figure every other problem out by these examples

Your text should help too. Math suddenly became easier for me when I stopped relying 100% on my professors, and started reading the book.