Question

Solve the following systems by forming the augmented matrix and reducing to reduced row echelon form. In each case decide whether the system has a unique solution, infinitely many solutions or no solution. Show pivots in squares. Describe the solution set.

-3x1+x2-x3=10

x2+4X3=12

-3x1+2x2+3x3=11

Answer 1

Step 1:

The Augmented Matrix Is given by:

Step 2

Make the pivot in the 1st column by dividing the 1st row by - 3

Step 3:

Eliminate the 1st column

Step 4:

Find the pivot in the 2nd column in the 2nd row

Step 5:

Eliminate the 2nd column

Thus, we note:

The system of equations corresponding to Reduced Row Echelon Form has as its 3nd equation:

i.e.,

0 = - 11

This shows that the given set of equations is inconsistent and has no solution.