Q:

Find a matrix A with $A \in M(6,4)$ with $\text{dim}(\text{ker}(A))=2$

Find a matrix A with $A \in M(6,4)$ with $\text{dim}(\text{ker}(A))=2$

Because $\text{dim}(\text{ker}(A)) + \text{dim}(\text{rg}(A))=$number of columns

$\rightarrow 2 + \text{dim}(\text{rg}(A)) = 4$ with $4$ form $M(6,4)$

$\leftrightarrow \text{dim}(\text{rg}(A))=2$

Can I say that $4$ is the number of columns?

Is that the right way to proceed?
If it is, how can I find this matrix?

A:

you are right and i think every matrix with 2 linear independence rows and 4 linear dependence(with that 2 before rows) other row also with 2 linear independence column and 2 other dependence (with 2 before column)column will be your answer

