Q2Multiple correct5 Marks15 Mar 2026

If $A$ is a $3\times4$ matrix and $b$ is a $3\times1$ matrix, then choose the set of correct options.

A

If $(A\mid b)$ is the augmented matrix and $(A'\mid b')$ is obtained from $(A\mid b)$ after a finite number of elementary row operations, then the systems $Ax=b$ and $A'x=b'$ have the same set of solutions.

B

If $(A'\mid b')$ is the reduced row echelon form of $(A\mid b)$, then the system $A'x=b'$ has at least one solution.

C

If $(A'\mid b')$ is the reduced row echelon form of $(A\mid b)$, then $A'$ is also in reduced row echelon form.

D

If $(A'\mid b')$ is the reduced row echelon form of $(A\mid b)$ and there is no row whose only non-zero entry lies in the last column of $(A'\mid b')$, then the system $Ax=b$ has at least one solution.