0 votes 0 votes MX = O is a homogeneous equation and such an equation when |M| = 0 has non trivial solution. M: Square Matrix O: Null Matrix Kindly help me with the above statement. Mathematical Logic engineering-mathematics linear-algebra matrix + – ryandany07 asked Aug 30, 2022 ryandany07 276 views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply shishir__roy commented Aug 30, 2022 reply Follow Share $M$ is a square matrix, say of size $n \times n$. Let $M$ has column vectors $m_1,m_2,...,m_n$ in $\mathbb{R}^n$. $|M| = 0 \implies$ column vectors of $M$ are linearly dependent. $\therefore c_1*m_1 + c_2*m_2 + ... + c_n*m_n = 0$, such that atleast one $c_i \neq 0$. $\implies Mx = 0$ has non-trivial solution. (Non-trivial means $x \neq 0$) 0 votes 0 votes ankitgupta.1729 commented Aug 31, 2022 reply Follow Share When $|M| = 0$ then system $MX=0$ is having both trivial and non-trivial solutions. You will always get the trivial solution for such a system whether $|M|$ is zero or not. 0 votes 0 votes Please log in or register to add a comment.