Q14Multiple correct3 Marks7 Jul 2024

Consider the system of linear equations $Ax=b$, where $A\in M_{n\times n}(\mathbb{R})$. Which of the following conditions guarantees that the system is consistent for any $b\in\mathbb{R}^n$? Select all true statements.

A

$A$ is a diagonal matrix with non-zero diagonal entries.

B

At least one column of $A$ is a linear combination of two other columns of $A$.

C

$b$ is one of the columns of $A$.

D

The reduced row echelon form of $A$ has no zero rows.

E

$A$ has at least $n-1$ linearly independent rows.