# Linear Transformation Problem

• Jun 17th 2013, 07:19 PM
generalkorn12
Linear Transformation Problem
Hi, I have trouble doing linear transformations from V->W an example:

(x,y,z) -> |y x|
..............|-z 0|

I tried doing:
T(1,0,0) = |0 1|
................|0 0|

T(0,1,0)= |1 0|
...............|0 0|

T(0,0,1= |0 0|
..............|-1 0|

but have no idea what to do next...
• Jun 18th 2013, 04:51 PM
chiro
Re: Linear Transformation Problem
Hey generalkorn12.

Hint: You are looking at a system which takes a 3x1 matrix to a 2x2 matrix. This means you will need for this setup a 2x3 and a 1x2 matrix for pre and post multiplication.

Can you expand this general system of matrix multiplications out and simplify this to get the specific elements in the 2x3 and 1x2 matrices?
• Jun 18th 2013, 05:28 PM
HallsofIvy
Re: Linear Transformation Problem
What do you mean by "doing" linear transformations? That is, what are the exact words of the problem?

(x, y, z)= x(1, 0, 0)+ y(0, 1, 0)+ z(0, 0, 1)
So T(x, y, z)= x T(1, 0, 0)+ y T(0, 1, 0)+ z T(0, 0, 1)

And you have already found T(1, 0, 0), T(0, 1, 0), and T(0, 0, 1).