Test B review, no calculators please help

Question

Answer 1

25)

The reduced row echelon form of matrix is

By using Gauss Jordan Elimination method,we got reduced row echelon form of matrix.

Number of variables n = 3

Rank of matrix A ( first 3 columns ) is R(A) = 2

Rank of echelon form  is R(AB) = 2

R(A) = R(AB) = 2 < n.

The system is consistent.

And system has infinitely many solutions.

z = 8

x + 3y = 7  ⇒  x = 7 - 3y

Solution : Option (b) is the correct choice.