Gaussian Elimination?

Question

Show that the system

x1 + x2 + x3 = y1
2*x1 + 3*x2 + x3 = y2
3*x1 + 5*x2 + x3 = y3

has an infinite number of solutions, provided that (y1, y2, y3) lies on the plane whose equation is y1 - 2*y2 + y3 =0.

Answer 1

Well, first you need to put it into a matrix.

[ 1 1 1 | y1]
[ 2 3 1 | y2]
[ 3 5 1 | y3]

then you need to proceed, by row operations, to turning this matrix into the unity matrix...
the row operations should give you a "solution" in terms of y1, y2, and y3.
if your solution is equal to the proposed solution. then you found your answer

Answer 2

Find out what y1-2y2+y3 is in terms of x1,x2 and x3. You get 0=0, which implies you don't have a basis for your y-space.