if the reduced row echelon form of the augmented matrix for a linear system has a row of zeros, then the system must have infinitely many solutions. true or false

False

Explanation:

If the row echelon form of the augmented matrix for a linear system has a row of zeros, then the there must not have infinitely many solution,

we can prove this with an example. Suppose we have an augmented matrix A for linear system with a row of zeros,

1 0 0 1

A = 0 1 0 - 2

0 0 1 - 1

0 0 0 0

we get

x1=1

x2=-2

x3=-1

so, system has an unique solution.

we can take inference that the given statement is wrong