Q1Multiple correct8 Marks21 Dec 2025

Let Ax = b represent a system of m linear equations in n variables. Choose the correct options.

A

Let A be an n x n matrix. If Ax = b has a unique solution, then adj(A)x = b also has a solution.

B

If Ax = b has a solution, then b is in Column space(A).

C

If $\text{rank}(A)$ = min(m, n), then Ax = b has a unique solution.

D

If $\text{rank}(A)$ = m, then there exists x in $\mathbb{R}^n$ such that Ax = b.

E

If the columns of A are linearly independent, then n > m.