Question 440213
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This matrix

{{{(matrix(3,4,
1, -1, 2, 8,
0, 1, -4, 2,
0, 0, 0, 0))}}}

represents this system of equations:

{{{system(1x-1y+2z=8,
0x+1y-4z=2,
0x+0y+0z=0)}}}

or written simpler:

{{{system(x-y+2z=8,
y-4z=2,
0z=0)}}}

The bottom equation

               0z = 0

has ANY real number as a solution.
Suppose the number k represents ANY
solution to 0z = 0, then  

                z = k

Substitute that into 

           y - 4z = 2

           y - 4k = 2

                y = 2 + 4k

Substitute z = k and y = 2 + 4k into

       x - y + 2z = 8

x - (2 + 4k) + 2k = 8

  x - 2 - 4k + 2k = 8

       x - 2 - 2k = 8

                x = 10 + 2k


So the solution is this ordered triple:

(x, y, z) = (10 + 2k, 2 + 4k, k)

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