- #1

- 37

- 0

x+ 2y - z + w - t = 0 \\

x - y + z + 3w - 2t = 0

\end{cases}

Add 1st to the 2nd:

$$2x + y + w - t = 0 \\

y = -2x -w + t = 0$$

Substitute y in the 1st:

##x + 2x + w - t + 3w - 2t + z = 0 \\

z = 3x - 4w + 3t##

Both z and y in terms of x,w,t. Writing using matrix form:

##\left[\begin{matrix}

x \\

y \\

z \\

w \\

t \\

\end{matrix}\right] =

x\left[\begin{matrix}

1 \\

-2 \\

-3 \\

0 \\

0 \\

\end{matrix}\right] +

w\left[\begin{matrix}

0 \\

-1 \\

-4 \\

1 \\

0 \\

\end{matrix}\right] +

t\left[\begin{matrix}

0 \\

1 \\

3 \\

0 \\

1 \\

\end{matrix}\right]

##

Solution ##x(1,-2,-3,0,0) + w(0,-1,-4,1,0) + t(0,1,3,0,1)##. I can isolate any two variables, but I have no idea if different solutions are in fact, part of the same set of solutions.