Show that the following system of equations is consistent. `x-y+z=3,2x+y-z=2,-x-2y+2z=1` Also, find the solution.

Explanation

We have given: `x-y+z=3,2x+y-z=2,-x-2y+2z=1`

As we know that the system of linear equation can be written in matrix form as `AX = B`

`implies A=|(1,-1,1),(2,1,-1),(-1,-2,2)|`,`X=[(x),(y),(z)]`,`B=[(3),(2),(1)]`

Now find the determinant of `A`,

`|A|= |(1,-1,1),(2,1,-1),(-1,-2,2)|`

`|A|=1(2−2)+1(4−1)+1(−4+1)`

`|A|=0`

Hence, `|A|=0 implies` the system of linear equation is consistent.

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