Determine whether the system is consistent or inconsistent. If it is consistent,give the solution.

Question

The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use x, y; or x, y, z; or x1, x2, x3, x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent,give the solution.

Answer 1

Step 1:

The reduced row echelon form of system of equation is

Number of variables .

Rank of the Matrix is 3.

Rank of the augmented matrix is 3.

Rank of = Rank of < , the system has infinitely many solutions.

Solution of the system of equations are

The solutions are

The solutions of the system of equations are .

Solution:

The system of equation is consistent.

The solutions of the system of equations are .