2 votes 2 votes Let $Ax = b$ be a system of linear equations where $A$ is a $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is a $n \times 1$ column vector of unknows. Which of the following is false? The system has a solution if and only if, both $A$ and the augmented matrix $[Ab]$ have the same rank. If $m < n$ and $b$ is the zero vector, then the system has infinitely many solutions. If $m = n$ and $b$ is non-zero vector, then the system has a unique solution. The system will have only a trivial solution when $m = n,$ $b$ is the zero vector and $rank (A) = n$. Linear Algebra go-mathematics-1 linear-algebra system-of-equations + – Bikram asked Aug 8, 2016 Bikram 448 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes "If m=n and b is non-zero vector, then the system has a unique solution" is FALSE actuallty. "If m=n and b is non-zero vector AND rank of matrix is also m, then the system has a unique solution" is TRUE. Digvijay Pandey answered Sep 12, 2016 Digvijay Pandey comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes c is correct as when m=n the matrix weill have unique soln. __ answered Aug 23, 2016 __ comment Share Follow See all 0 reply Please log in or register to add a comment.