Question

The reduced row-echelon forms of the augmented matrices of four systems are given below. How many solutions does each system have? Here is the matrices:
1 0 -12 0
0 1 0 0
0 0 0 1
0 0 0 0
A. Infinitely many solutions
B. No solutions
C. Unique solution
D. None of the above

Answer 1

Answer:

A. Infinitely many solutions.

Step-by-step explanation:

The row and column numbers are equal in the echelon. This rows have 0001 numbers which indicates that there is free variable at the end. The reduced row echelon has equal number of rows and columns. There are infinitely many solution as the numbers in the rows are zero ending of the free variable 1. If there is no free variable then there will be no solution.