Solve the following system of equations Enter your answers a

Solve the following system of equations. (Enter your answers as a comma-separated list. If there are infinitely many solutions, enter a parametric solution using t and/or s. If there is no solution, enter NONE.) 3y + 2z = 1 2x y 3z = 2 2x + 2y z = 3

Solution

3y+2z=1

2x-y-3z=2

2x+2y-z=3

Using Gauss-Jordan elimination to change this to reduced row-echelon form:

( 0 3 2 2

2 -1 -3 2

2 2 -1 3 )

3x² + 2x₃ = 1

3x2+3x3+x4=0

2x1-x2-3x3+2x4=0

2x1+2x2-x3+3x4=0

x1=-3s-t

x2=+ S

x3= 3t

x4= - 3t