Q18Multiple correct2 Marks20 Nov 2022

Which of the following options are true?

A

If $A$ is a non-zero matrix of order $4\times3$ and $\operatorname{rank}(A)=3$, then the rows of $A$ are linearly independent.

B

If $A$ is a non-zero matrix of order $4\times3$ and $\operatorname{rank}(A)=3$, then the columns of $A$ are linearly independent.

C

If $A$ is a non-zero matrix of order $m\times(m+1)$, $m>1$, then the maximum possible nullity of $A$ is $m$.

D

If $A$ is a non-zero matrix of order $4\times5$ and $\operatorname{rank}(A)=3$, then the dimension of the solution space of $Ax=0$ is $2$.