Prove linear transformation is one to one The linear operator T: R2→R2 defined by the equations 
w1 = 4x1 - 6x2 
w2 = -2x1 + 3x2
is not one-to-one.  Using the methods in class, show why this is true. Once you have done this, provide a simple, specific,  numerical example, where the output vector is not the zero vector, that illustrates why the transformation is not one-to-one. 
Okay, so I was able to answer the first part (proving the transformation is not one to one). 
But for the second part, I'm not exactly sure what to do. Do I just give any input vector that produces a nonzero output? 

You are suppose to find $x_1, x_2, y_1, y_2$ such that $(x_1, x_2) \neq (y_1, y_2), (w_1, w_2) \ne (0,0),$ and
$$4x_1-6x_2=w_1 = 4y_1-6y_2$$
$$-2x_1+3x_2=w_2 = -2y_1+3y_2$$
