Homework Help: Row space of a transformation matrix

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1. Sep 28, 2016

GwtBc

1. The problem statement, all variables and given/known data
We're given some linear transformations, and asked what the null space, column space and row space of the matrix representations tell us
2. Relevant equations

3. 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?

2. Oct 4, 2016

Greg Bernhardt

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Oct 4, 2016

Staff: Mentor

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.