Solve the following system of linear equations by Cramers rule: `x+y=1,\ \ \ x+z=-6,\ \ \ x-y-2z=3`

Explanation

We have given:`x+y=1,\ \ \ x+z=-6,\ \ \ x-y-2z=3`

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

`implies A=|(1,1,0),(1,0,1),(1,-1,-2)|`,`X=[(x),(y),(z)]`,`B=[(1),(-6),(3)]`

Now find the determinant of `A`,

`|A|= |(1,1,0),(1,0,1),(1,-1,-2)|`

`|A|=1[(0)( – 2) – (1)( – 1)] – 1[( – 2)(1) – 1] + 0[ – 1 – 0]`

`|A|=1+3 + 0`

`|A|=Delta=4`

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