Solve the given system of equations using either Gaussian or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION.)x1 − 3x2 − 2x3 = 0−x1 + 2x2 + x3 = 02x1 + 3x2 + 5x3 = 0

The system has infinitely many solutions

Step-by-step explanation:

Gauss–Jordan elimination is a method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

An Augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

There are three elementary matrix row operations:

To solve the following system

Step 1: Transform the augmented matrix to the reduced row echelon form

This matrix can be transformed by a sequence of elementary row operations

Row Operation 1: add 1 times the 1st row to the 2nd row

Row Operation 2: add -2 times the 1st row to the 3rd row

Row Operation 3: multiply the 2nd row by -1

Row Operation 4: add -9 times the 2nd row to the 3rd row

Row Operation 5: add 3 times the 2nd row to the 1st row

to the matrix

The reduced row echelon form of the augmented matrix is

which corresponds to the system

The system has infinitely many solutions.

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