Linear Transformations

Find the matrix associated with the following linear transformation:

T: R^3 -> R^2
given by
T(x,y)^T = (x+y, x-y; 3y)^T , where ^T is transposed.

How do I do this?

Did you mean $\displaystyle T : \mathbb R^2 \mapsto \mathbb R^3$ ?

So you need a matrix A that satisfies:

$\displaystyle A_{3\times 2}\begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} x+y\\x-y\\3y \end{bmatrix}$

Does that make things easier?

Quote:

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Originally Posted by scorpion007

Did you mean $\displaystyle T : \mathbb R^2 \mapsto \mathbb R^3$ ?

So you need a matrix A that satisfies:

$\displaystyle A_{3\times 2}\begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} x+y\\x-y\\3y \end{bmatrix}$

Does that make things easier?

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No it is not R^3--> R^2? I attached the file, it's number 4.a
Maybe it is a typo?