Question

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

Answer 1

Answer:

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