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#### karush

##### Well-known member

- Jan 31, 2012

- 2,928

Find a basis for

just seeing if these first steps are correct

\(\displaystyle \begin{align*}

A_{15}&=\left[

\begin{array}{rrr} -4&1&1\\ 2&-3&2\\ 3&3&-2 \end{array}

\right],\lambda=-5&(1)\\

A-(-5)i&=\left[

\begin{array}{rrr} -4&1&1\\ 2&-3&2\\ 3&3&-2 \end{array}

\right]-

\left[

\begin{array}{rrr} -5&0&0\\ 0&-5&0\\ 0&0&-5

\end{array}\right]=&(2)\\

&=\left[

\begin{array}{rrr} 1&1&1\\ 2&2&2\\ 3&3&3 \end{array}

\right]&(3)

\end{align*}\)

$$\tiny{311.05.01.15;

Linear Algebra \, and \, its \, Applications; \, David \, C Lay; \, 4th \,Edition}$$

*eigenspace*corresponding to the listed*eigenvalue*:just seeing if these first steps are correct

\(\displaystyle \begin{align*}

A_{15}&=\left[

\begin{array}{rrr} -4&1&1\\ 2&-3&2\\ 3&3&-2 \end{array}

\right],\lambda=-5&(1)\\

A-(-5)i&=\left[

\begin{array}{rrr} -4&1&1\\ 2&-3&2\\ 3&3&-2 \end{array}

\right]-

\left[

\begin{array}{rrr} -5&0&0\\ 0&-5&0\\ 0&0&-5

\end{array}\right]=&(2)\\

&=\left[

\begin{array}{rrr} 1&1&1\\ 2&2&2\\ 3&3&3 \end{array}

\right]&(3)

\end{align*}\)

$$\tiny{311.05.01.15;

Linear Algebra \, and \, its \, Applications; \, David \, C Lay; \, 4th \,Edition}$$

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