Hints:
For this this linear system to have a solution:
x3 = 5-x1-3x2
x4 = (1-x1-x2)/2
Also try to solve using least squares when number of unknowns and equations are not equal...to obtain:
{x1, x2, x3, x4} = {17/50, 69/50, 13/25, -9/25}
Find the general solution to the following system of equations and indicate which variables are free and which are basic.
Putting it in augmented matrix form to start we have:
1 -1 -1 4 | -3
1 0 -1/2 3 | -1
1 1 0 2 | 1
Now performing the following fundamental row operations:
R1<-->R2
R2+R3-->R2
-2R3+R2-->R2
-R3+R1-->R3
R2/-2
R2+R3-->R2
-3R3+R1-->R1
And finally I end with the augmented matrix:
1 0 -2 0 | 5
0 1 0 0 | 0
0 0 -1/2 1 |-2
Can someone please tell me if I got the correct matrix at the end and if so how do I determine which variables are free and which are basic?
Thank you.
Hints:
For this this linear system to have a solution:
x3 = 5-x1-3x2
x4 = (1-x1-x2)/2
Also try to solve using least squares when number of unknowns and equations are not equal...to obtain:
{x1, x2, x3, x4} = {17/50, 69/50, 13/25, -9/25}