Question

Consider a linear homogeneous system of equations $Ax = 0$, where $A$ is an $n \times n$ matrix, $x$ is an $n \times 1$ vector, and $0$ is an $n \times 1$ null vector. Let $r$ be the rank of $A$. For a non-trivial solution to exist, which of the following conditions is/are satisfied?

• A. Determinant of $A = 0$
• B. $r = n$
• C. $r < n$
• D. Determinant of $A$ \neq$$ 0

Answer 1

Answer: (A), (C)

Determinant of $A = 0$

Answer 2

The correct Answer are (A) :Determinant of $A = 0$, (C):$r < n$