List of top Engineering Mathematics Questions on Matrix algebra

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?