Solve the following system of linear equations by Cramers rule: `2x-3y-4z=29 ,\ -2x+5y-z=-15 ,\ \ 3x-y+5z=-11`

Explanation

We have given:`2x-3y-4z=29 ,\ -2x+5y-z=-15 ,\ \ 3x-y+5z=-11`

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

`implies A=|(2,-3,-4),(-2,5,-1),(3,-1,5)|`,`X=[(x),(y),(z)]`,`B=[(29),(-15),(-11)]`

Now find the determinant of `A`,

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

`|A|=2[(5)(5) – ( – 1)( – 1)] – ( – 3)[( – 2)(5) – 3( – 1)] + ( – 4)[( – 2)( – 1) – 3(5)]`

`|A|=48 – 21 + 52`

`|A|=Delta=79`

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