Question

Row Reduce {{-7,4,2,0},{4,-7,-2,0},{0,0,0,0}}
I know the answer is {{1,0,-2/11,0},{0,1,2/11,0},{0,0,0,0}} but please show me the steps to get there.

Answer 1

\[\left( \begin{array}{cccc} -7 & 4 & 2 & 0 \\ 4 & -7 & -2 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right)\]
this one?

Answer 2

yes

Answer 3

\[ \left[\begin{matrix} -7 & 4 & 2 & 0 \\ 4 & -7 & -2 & 0 \\ 0 & 0 & 0 & 0 \end{matrix}\right] \cong \left[\begin{matrix} -7 & 4 & 2 & 0 \\ -3 & -3 & 0& 0 \\ 0 & 0 & 0 & 0 \end{matrix}\right]\cong \left[\begin{matrix} -7 & 4 & 2 & 0 \\ 1 & 1 & 0& 0 \\ 0 & 0 & 0 & 0 \end{matrix}\right]\]\[\cong \left[\begin{matrix} 1 & 1 & 0& 0 \\ -7 & 4 & 2& 0 \\ 0 & 0 & 0 & 0 \end{matrix}\right]\cong \left[\begin{matrix} 1 & 1 & 0& 0 \\ 0 & 11 & 2& 0 \\ 0 & 0 & 0 & 0 \end{matrix}\right]\]

Answer 4

Operationally:

R1+R2 -> R2
(-1/3)R2 -> R2
R1 <-> R2
7R1 + R2 -> R2

Answer 5

The trick is to look for things you can make 0.

Answer 6

Funny, those are the exact steps I did, the only problem is I am having trouble getting it to row reduced echelon form. I'll figure it out, eventually. Thanks for your help.

Answer 7

Oh, you need reduced row

Answer 8

I got it! Thanks

Answer 9

\[\cong\left[\begin{matrix} 1 & 0 & -\frac{2}{11} & 0 \\ 0 & 1 & \frac{2}{11}& 0 \\ 0 & 0 & 0 & 0 \end{matrix}\right]\]

Answer 10

yup! I solved the problem already. Thanks for you help

Answer 11

Great job.

Answer 12

You too.