If the system x1 x2 x3 x4 3 2x1 x3 0 x1 x2 2x3 1 3x

If the system {x_1 + x_2 - x_3 - x_4 = 3 2x_1 + x_3 = 0 x_1 + x_2 + 2x_3 = 1 3x_1 - x_2 - x_3 + x_4 = -1 is solved, what is the value of x_2? Use Cramer\'s rule.

Solution

Your matrix

Write down the main matrix and find its determinant

D = -8

Replace the 1st column of the main matrix with the solution vector and find its determinant

D1 = -2

  

Replace the 2nd column of the main matrix with the solution vector and find its determinant

D2 = -14

Replace the 3rd column of the main matrix with the solution vector and find its determinant

D3 = 4

  

Replace the 4th column of the main matrix with the solution vector and find its determinant

D4 = 4

x1 = D1 / D = (-2) / (-8) = 1/4

x2 = D2 / D = (-14) / (-8) = 7/4

x3 = D3 / D = 4 / (-8) = -1/2

x4 = D4 / D = 4 / (-8) = -1/2

solution

x1 = 1/4

x2 = 7/4 (Answer)

x3 = -1/2

x4 = -1/2

	X1	X2	X3	X4	b
1	1	1	-1	-1	3
2	2	0	1	0	0
3	1	1	2	0	1
4	3	-1	-1	1	-1