Question

Linear Algebra - Linear Transformations?
When you represent a 3-D object graphically in the plane (on paper, the blackboard, etc.) you have to transform spacial coordinates, [x1,x2,x3], into plane coordinates, [y1,y2]. The simplest choice is a linear transformation, for example the one given by [(-1/2 1 0), (-1/2 0 1)] (This is a matrix, the top row being -1/2 1 0 and the bottom row being -1/2 0 1).
(a) Use this transformation to represent the unit cube with corner points [0,0,0]; [1,0,0]; [0,1,0]; [0,0,1]; [1,1,0]; [1,0,1]; [1,1,1]. Include the images of the x1, x2, and x3 axes in your sketch.
(b) Represent the image of the point [1,1/2,1/2] in your figure in part a. Explain.
(c) Find all points [x1,x2,x3] that are transformed to [0,0]. Explain.

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Notes:
[x1,x2,x3] and all similar notations are column vectors in matrix form, I just don't know how to write them in yahoo answers.
You don't have to actually draw a sketch, just explain enough so that I can.
Even if someone can only do one of the parts, any help is appreciated.

THANK YOU SO MUCH!!!!! GRACIAS! DANKE! (: