I need some help with a linear algebra question If you could

I need some help with a linear algebra question. If you could explain to me the problem and steps and show it on paper, that would be great. Thank you!

Solution

All you have to do is to recognize that T(x1,x2,x3)=AX=w
Thus from the given transformation, you can pick up your standard matrix.
Just pick respective x1,x2,x3 values from the x-coordinate ,

I mean:
x1-2x2 =x1-2x2+ox3 --> (1,-2,0)is your first row of your standard matrix
x2+x3=0x1+x2+x3--> (0,1,1) is your second row of your standard matrix

Thus Matrix is:
1 -2 0
0 1 1

it is one-to-one and onto function.