Solve the following system of linear equations by Cramers rule: `x-4y-z=11 ,\ \ \ 2x-5y+2z=39 ,\ \ -3x+2y+z=1`

Explanation

We have given:`x-4y-z=11 ,\ \ \ 2x-5y+2z=39 ,\ \ -3x+2y+z=1`

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

`implies A=|(1,-4,-1),(2,-5,2),(-3,2,1)|`,`X=[(x),(y),(z)]`,`B=[(11),(39),(1)]`

Now find the determinant of `A`,

`|A|= |(1,-4,-1),(2,-5,2),(-3,2,1)|`

`|A|=1(-5−4)-(-4)(2+6)+(-1)(4-15)`

`|A|=-9+32+22`

`|A|=Delta=34`

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