- #1

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- 31

## Homework Statement

The matrix,A,given by

[tex]

A = \left(

\begin{array}{ccc}

7 & -4 & 6\\

2 & 2 & 2 \\

-3 & 4 & -2 \

\end{array}

\right)

[/tex]

has eigenvalues 1,2,4 . Find a set of corresponding eigenvectors.

Hence find the eigenvalues of B, where

[tex]

B = \left(

\begin{array}{ccc}

10 & -4 & 6\\

2 & 5 & 2 \\

-3 & 4 & 1 \

\end{array}

\right)

[/tex]

and state a corresponding set of eigenvectors.

## Homework Equations

## The Attempt at a Solution

Well I easily found the eigenvectors

[itex]

\lambda=1[/itex] corresponds to

[tex]

\left(

\begin{array}{c}

-1\\

0 \\

1\

\end{array}

\right)

[/tex]

[itex]

\lambda=2[/itex] corresponds to

[tex]

\left(

\begin{array}{c}

-4\\

1 \\

4\

\end{array}

\right)

[/tex]

[itex]

\lambda=4[/itex] corresponds to

[tex]

\left(

\begin{array}{c}

2\\

3 \\

1\

\end{array}

\right)

[/tex]

Well for the one with B, just solve det(b-[itex]\lambda[/itex]I)=0 to get the e.values... but it says to state a set of e.vectors meaning that I am not supposed to work them out.

The only thing I can really say about A and B is that in B all the elements in the main diagonal are the elements in the main diagonal of A with 3 added to them