Question

How do you solve `-x + y + z = -1` and `-x + 5y - 15z = -13` and `3x - 2y - 7z = 0` using matrices?

Answer 1

This is a impossible system of equations and has no solution.

Explanation:

`Delta=[[-1,1,1],[-1,5, -15],[3,-2,-7]]=35-45+2-(15-30+7)=-8+8=0`
`Delta x=[[-1,1,1],[-13,5, -15],[0,-2,-7]]=35+0+26-(0-30+91)=61-61=0`
`Delta y=[[-1,-1,1],[-1,-13, -15],[3,0,-7]]=-91+45+0-(-39-7+0)=-46+46=0`
`Delta z=[[-1,1,-1],[-1,5, -13],[3,-2,0]]=0-39-2-(15-26+0)=-41+11=-10`

Since `Delta =0` but `Delta z !=0` this system of equations is a impossible one and has no solution.