# Thread: Matrix and Linear Mapping

1. ## Matrix and Linear Mapping

$\displaystyle h: {\mathbb{R} }^3 \rightarrow {\mathbb{R} }^2$ is given by $\displaystyle h(x,y,z) =(7x, y-z)$ is a linear mapping.

For this function, write down its matrix with respect to the standard bases of the domain and codomain.

I took this to mean $\displaystyle h_A (\bold{x} ) = A \bold{x} = A \begin{bmatrix} x\\ y \\ z \\ \end{bmatrix} = \begin{bmatrix} 7x \\ y-z\\ \end {bmatrix}$

where $\displaystyle A = \begin{bmatrix} 7 & 0 & 0 \\ 0 & 1 & -1 \\ \end{bmatrix}$. But how do I write this down with respect to the standard bases of the domain and codomain. I know these are (1,0,0), (0,1,0), (0,0,1) , (1,0), (0,1). Thanks very much.

2. hehe, I think you alrady did write it with respect to the standard basis, since

$\displaystyle h(1,0,0)=(7,0); h(0,1,0)=(0,1); h(0,0,1)=(0,-1)$

and that`s, by definition, hoy you find the associate matrix of a linear transformation: "hanging" the vectors which result of finding the images of the standard basis by the transformation.
So A itself is the matrix you are looking for...

I hope that will be useful.

3. ok thank you, I usually know what to do in questions like this but the lingo confuses me hehe