[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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Rowspace and kernel

**Physics Forums | Science Articles, Homework Help, Discussion**