# Homework Help: Linear Transformation matrix help

1. Feb 16, 2010

### cwatki14

The problem is as follows:
Find a nonzero 2x2 matrix A such that Ax is parallel to the vector
[1]
[2]
for all x in R2.

So far I know A=[v1 v2] therefore Ax= [v1 v2][x1]
[x2]

= x1v1+x2v2
I know these two vectors are parallel, but I am a little stuck how to relate this property to solve for the matrix A.

2. Feb 17, 2010

### Staff: Mentor

You have Ax = k[1 2]T for any vector x in R2.
Specify values for A.

What does A do to [1 0]T? to [0 1]T?

3. Feb 17, 2010

### HallsofIvy

What Mark44 suggests works fine. A more "primitive method" is to write A as
$$\begin{bmatrix}a & b \\ c & d\end{bmatrix}$$
so your equation "Ax= k[1 2]T" becomes
$$\begin{bmatrix}a & b \\ c & d\end{bmatrix}$$\begin{bmatrix} x \\ y\end{bmatrix}= \begin{bmatrix}ax+ by \\ cx+ dy\end{bmatrix}= \begin{matrix}k \\ 2k\end{bmatrix}[/tex]

giving you two equations, ax+ by= k and cx+ dy= 2k for the 5 unknown numbers. There will, of course, be an infinite number of possible answers. You are simply asked to find one such matrix.

4. Feb 17, 2010