Show that following system of linear equations is inconsistent: `4x-5y-2z=2,\ \ 5x-4y+2z=-2,\ \ 2x+2y+8z=-1`

Explanation

We have given: `4x-5y-2z=2,\ \ 5x-4y+2z=-2,\ \ 2x+2y+8z=-1`

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

`implies A=|(4,-5,-2),(5,-4,2),(2,2,8)|`,`X=[(x),(y),(z)]`,`B=[(2),(-2),(-1)]`

Now find the determinant of `A`,

`|A|= |(4,-5,-2),(5,-4,2),(2,2,8)|`

`|A|=4(-36)+5(36)-2(18)`

`|A|=0`

Hence, `|A|=0 implies A` is singular.

...