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## Homework Statement

Find the Eigenspace of the following matrix:

[tex]\begin{bmatrix}

1 & 3 \\

4 & -3

\end {bmatrix}[/tex]

I'm skipping a few steps but the Eigenvalues are -5 and 3. Let's starts with -5. Skip a few more steps, I know I'm right, just trust me.

We now have the following matrix:

[tex]\begin{bmatrix}

-6 & -3 \\

-4 & -2

\end {bmatrix}[/tex]

Then you find the null space, which starts with putting it in reduced row echelon form:

[tex]\begin{bmatrix}

-6 & -3 \\

0 & 0

\end {bmatrix}[/tex]

you can reduce that further to

[tex]\begin{bmatrix}

-2 & -1 \\

0 & 0

\end {bmatrix}[/tex]

This is where I'm confused. This nullspace calculator http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi

says that the basis of the null space is

[tex]\begin{bmatrix}

-1 \\

2

\end {bmatrix}[/tex]

My textbook confirms that. How do I get from here

[tex]\begin{bmatrix}

-2 & -1 \\

0 & 0

\end {bmatrix}[/tex]

to there

[tex]\begin{bmatrix}

-1 \\

2

\end {bmatrix}[/tex]

I would think you would just eliminate the 2nd row and transpose the first row but that would give.

[tex]\begin{bmatrix}

-2 \\

-1

\end {bmatrix}[/tex]

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