SOLUTION: Solve the system 5x1 - 6x2 + 3x3 + 4x4 = 4 -x1 + x2 + 3x3 + 2x4 = 5 4x1 - 5x2 + 6x3 + 6x4 = 9 -3x1+ 3x2 + 9x3 + 6x4 = 15

Question 1159570: Solve the system
5x1 - 6x2 + 3x3 + 4x4 = 4
-x1 + x2 + 3x3 + 2x4 = 5
4x1 - 5x2 + 6x3 + 6x4 = 9
-3x1+ 3x2 + 9x3 + 6x4 = 15

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Your matrix

its determinant Δ =
This means that the system of linear equations is either inconsistent or has infinitely many solutions. Gauss-Jordan elimination method will help get the complete answer.
Find the pivot in the 1st column (inversing the sign in the whole row) and swap the 2nd and the 1st rows

Multiply the 1st row by 5

Subtract the 1st row from the 2nd row and restore it

Multiply the 1st row by 4

Subtract the 1st row from the 3rd row and restore it

Multiply the 1st row by -3

Subtract the 1st row from the 4th row and restore it

Find the pivot in the 2nd column in the 2nd row (inversing the sign in the whole row)

Multiply the 2nd row by -1

Subtract the 2nd row from the 1st row

Subtract the 2nd row from the 3rd row and restore it

Solution set:

, - free

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