True or False A linear system is consistent if and only if t

True or False

A linear system is consistent if and only if there are free variables in the row-echelon form of the corresponding augmented matrix.

Solution

False.

Beacuse uniqueness theorem states that

If a linear syetem is consistent then solution set contains either,

(a) a uniques solution, when there are no free variables, or

(b) infinitely many solutions when there is at least one free variable.

SO even there is no free variables in the system there can be a linear system that is consistent.