Show that the following systems of linear equations has infinite number of solutions and solve `2x+y-2z=4,\ \ x-2y+z=-2,\ \ 5x-5y+z=-2`

Explanation

We have given systems of linear equations`2x+y-2z=4,\ \ x-2y+z=-2,\ \ 5x-5y+z=-2`

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

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

Now find the determinant of `A`,

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

`|A|=Delta=2(-2+5)-1(1-5)-2(-5+10)=0`

Now as `B=[(4),(-2),(-2)]`

Then

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