Finding kernel of matrix transformation

[DWill]

Homework Statement

Find the kernel of the matrix transformation given by f(x) = Ax, where

A =
1 -1 0
0 1 -2

(it's a matrix)

Homework Equations

Kernel is the set x in R^n for f(x) = Ax = 0

The Attempt at a Solution

I set up the problem like this:

[
X1
X2 * A = 0
X3
]

Just multiplying the matrices I get:

X1 - X2 = 0
X2 - 2X3 = 0

I think I'm missing something really simple but I'm stuck on what to do now in solving the system of equations for X1, X2, X3. Any hints, suggestions, or corrections? thanks

 

[Defennder]

You have that system of homogenous linear equations. Now represent in a form of a matrix and reduce it to its reduced row echelon form. Then you can read off the values of x1,x2,x3. Denote variables by parameters if you have to.

 

[gabbagabbahey]

You have two equations and three unknowns, so you are going to have at least one free parameter, you may as well pick X3=t for your parameter and solve for X1 and X2 in terms of t.