Using matrices, solve the following system of linear equations: `x\ -\ y+2z=7` `3x+4y\ -\ 5z=-5` `2x\ -\ y+3z=12`

Explanation

We have given: `x\ -\ y+2z=7`
`3x+4y\ -\ 5z=-5`
`2x\ -\ y+3z=12`

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

`implies A=|(1,-1,2),(3,4,-5),(2,-1,3)|`,`X=[(x),(y),(z)]`,`B=[(7),(-5),(12)]`

Now find the determinant of `A`,

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

`|A|=1(12−5)+1(9+10)+2(−3−8)`

...