[tex]A = \left(\begin{array}{cccc}-1 &6&5&9 \\ -1&0&1&3 \end{array}\right)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Find orthonormal bases of the kernel, row space.

To find the bases, I did reduced the array to its RREF.

[tex]A = \left(\begin{array}{cccc}1 & 0&-1&-3\\ 0&1&2/3&1 \end{array}\right)[/tex]

Then the orthonormal bases would just be that divided by the length.

[tex]||v_1||=\sqrt{1+1+3^2}=\sqrt{11}[/tex]

[tex]||v_2||=\sqrt{1+(2/3)^2+1}=\sqrt{2.44444}[/tex]

so that means, the orthonormal bases would be:

[tex]A = \left(\begin{array}{cccc} \frac{1}{ \sqrt{11}} & 0&\frac{-1}{ \sqrt{11}}&\frac{-3}{ \sqrt{11}} \\0 & \frac{1}{ \sqrt{2.44444}} & \frac{.66666}{ \sqrt{2.44444}} &\frac{1}{ \sqrt{2.44444}}\end{array}\right)[/tex]

what exactly is the orthonormal bases of the kernel?

Also, isnt the row space the same as the vectors of the bases?

I think I also did something wrong in my calculations

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# Rowspace and kernel

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