16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 2.6.7
Vector Spaces
Mathematics — Linear Algebra · consistency-condition-for-linear-system
Problem
Let A be an m×n matrix over the field F, and consider the system of equations AX=Y. Prove that this system of equations has a solution if and only if the row rank of A is equal to the row rank of the augmented matrix of the system.