Show that the following systems of linear equations has infinite number of solutions and solve `x-y+z=3,\ \ \ 2x+y-z=2,\ \ -x-2y+2z=1`

Explanation

We have given systems of linear equations `x-y+z=3,\ \ \ 2x+y-z=2,\ \ -x-2y+2z=1`

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

`implies A=|(1,-1,1),(2,1,-1),(-1,-2,2)|`,`X=[(x),(y),(z)]`,`B=[(6),(2),(1)]`

Now find the determinant of `A`,

`|A|=|(1,-1,1),(2,1,-1),(-1,-2,2)|`

`|A|=Delta=1(2-2)+1(4-1)+1(-4+1)=0`

Now as `B=[(3),(2),(1)]`

Then

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