Question

Describe the domain and range of the linear transformation defined by the matrix

A=(1 3; 1 1; 2 3)

What is the rank of matrix A?

Answer 1

2

Answer 2

Is it because there are two rows in the matrix?

Answer 3

rank = min(m,n)

if you had
\[\left[\begin{matrix}1 & 3 & 1 \\ 1 & 2 &3\end{matrix}\right]\]
what will you get?

Answer 4

I've actually never learned rank, I'm trying to help friends study for test and it's covering some material I haven't done :/

Answer 5

I have to run to a meeting, but I'll be back on in an hour or so. Thanks again, I appreciate all the help :)

Answer 6

rank is the min (row, column) of the nonzero rows
\[\left[\begin{matrix}1 & 1 \\ 0 & 0\end{matrix}\right]\rightarrow rank = 1 \]
you had 2rows and two columns put a row full of zeros so it will be 1 row and 2 columns; the min is 1

\[\left[\begin{matrix}1 & 0 & 3 & 4\\ 0 & 0 & 5 & 6 \\ 1 & 0 & 9 & 7 \\0 & 0 &1 & 0 \end{matrix}\right]\rightarrow rank =3 \]
you had 4rows and 4 columns put a column full of zeros so it will be 4 row and 3 columns; the min is 3

do you understand it now?

Answer 7

I think so, thanks :)