Show that the following systems of linear equations are inconsistent: `3x-y+2z=3,\ \ 2x+y+3z=5,\ \ x-2y-z=1`

Explanation

We have given systems of linear equations `3x-y+2z=3,\ \ 2x+y+3z=5,\ \ x-2y-z=1`

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

`implies A=|(3,-1,2),(2,1,3),(1,-2,-1)|`,`X=[(x),(y),(z)]`,`B=[(3),(5),(1)]`

Now find the determinant of `A`,

`|A|=|(3,-1,2),(2,1,3),(1,-2,-1)|`

`|A|=Delta=15-5-10=0`

Now as `B=[(3),(5),(1)]`

Then

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