Row space of a transformation matrix

[GwtBc]

Homework Statement

We're given some linear transformations, and asked what the null space, column space and row space of the matrix representations tell us

Homework Equations

The Attempt at a Solution

I know what information the column space and null space contain, but what does the row space of a transformation matrix tell me?

 

[Mark44]

Homework Statement

We're given some linear transformations, and asked what the null space, column space and row space of the matrix representations tell us

Homework Equations

The Attempt at a Solution

I know what information the column space and null space contain, but what does the row space of a transformation matrix tell me?

The row space is a subspace of the domain of the transformation.
Here's a simple example.
Let T be a linear transformation, $T: R^3 \to R^2$, with T(x) = Ax, with x in R³ and A defined as
$A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \end{bmatrix}$
The row space of A is a two-dimensional subspace of R³; namely, the x-y plane. This transformation projects a vector x onto the x-y plane.