Kunze Linear Algebra · Problem 2.6.7

Vector Spaces

Mathematics — Methods · consistency-of-linear-system

Problem

Let

A

be an

m \times 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.