$3 x+3 y+2 z=1, x+2 y=4,10 y+3 z=-2,2 x-3 y-z=5$ are consistant and obtain the solutions for $\mathrm{x}, \mathrm{y}$ and z . $$ \left[\begin{array}{ccc} 2 & 3 & -2 \\ -2 & 1 & 1 \\ 1 & 0 & 2 \end{array}\right] $$
Explanation
To check if a system of linear equations is consistent, we need to check if the rank of the coefficient matrix is equal to the rank of the augmented matrix. If they are equal, then the system is consistent.
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