Answer
infinitely many solutions
Work Step by Step
In a square system, if Gaussian elimination results in a matrix with a row with all 0s,the system has an infinite number of solutions (contains dependent equations).
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The last row represents the equation
0=0,
which is true for any triplet (x,y.z).
The other two equations will define the relationships between x, y, and z.
There will be infinitely many solutions.
This is how:.
We take z to be any real number, and back-substitute into row 2,
$z=t,\quad t\in \mathbb{R},$
$y=-1+10t$
Back substituting both into row 1,
$x=2+(-1+10t)+2t=12t+1$
And the solution set is
$\{(12t+1, 10t-1, t),\quad t\in \mathbb{R}\} $
(The system has as many solutions as $\mathbb{R}$ has numbers)
