Question

Find a general solution solution of the homogeneous system [1 2 1; -2 1 -7; 3 4 5][x1 x2 x3] = [0 0 0]

Answer 1

this is what i got

Answer 2

I got the same!
so, the solution should look like:
|-3*x3 |
x= | x3 |
| x3 |

it's one column matrix where is x3 is any number

Answer 3

Or you can write it as\[x = \left[ \begin{array}{c} -3\\1 \\1 \end{array} \right]x_3\implies x \in Span \{\left[ \begin{array}{c} -3\\1 \\1 \end{array} \right]\}\]

Answer 4

yes i forgot the pretty things that we can write
gj inink and polpak