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?

Question

cdquestions Admin · Accepted Answer

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

Answer

Determinant of $ A = 0 $

Answer

Answer

Answer

Determinant of $ A $ $\neq$$ 0 $

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?

The Correct Option is A, C

Solution and Explanation

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