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suspenc3

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Find the Eigenvalues of the matrix and a corresponding eigenvalue. Check that the eigenvectors associated with the distinct eigenvalues are orthogonal. Find an orthogonal matrix that diagonalizes the matrix.

(1)[tex]\left(\begin{array}{cc}4&-2\\-2&1\end{array}\right)[/tex]

I found my eigenvalues to be 5 & 0, and the corresponding eigenvectors to be

[tex]\left(\begin{array}{cc}-2\\1\end{array}\right)[/tex]

and

[tex]\left(\begin{array}{cc}1/2\\1\end{array}\right)[/tex]

The book doesn't really explain this section well, can someone help me out with what to do next?

Also, how do you know if the eigenvectors produce an orthogonal set of vectors?what is orthonormal?

Thanks

(1)[tex]\left(\begin{array}{cc}4&-2\\-2&1\end{array}\right)[/tex]

I found my eigenvalues to be 5 & 0, and the corresponding eigenvectors to be

[tex]\left(\begin{array}{cc}-2\\1\end{array}\right)[/tex]

and

[tex]\left(\begin{array}{cc}1/2\\1\end{array}\right)[/tex]

The book doesn't really explain this section well, can someone help me out with what to do next?

Also, how do you know if the eigenvectors produce an orthogonal set of vectors?what is orthonormal?

Thanks

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