a Use Cramers rule to solve the system of linear equations x

a) Use Cramer\'s rule to solve the system of linear equations x_1 + 5x_2 = 7 -2x_1-7 x_2 = -5 b) Use Gauss elimination with pivoting to solve the system of linear equations 2x_2 + x_3 = -8 x_1 - 2x_2 - 3x_3 = 0 -x_1 + x_2 + 2x_3 = 3 c) Use Gauss-Seidel method with pivoting if necessary to solve the system of linear equations 4x_1 - x_2 + x_3 = 12 -x_1 + 4x_2 - 2x_3 = -1 x_1 - 2 x_2 + 4 x_3 = 5

Solution

a)

Your matrix

Write down the main matrix and find its determinant

D = 3

Very detailed solution  

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

D1 = -24

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

D2 = 9

Very detailed solution  

x1 = D1 / D = (-24) / 3 = -8

x2 = D2 / D = 9 / 3 = 3

solution

x1 = -8

x2 = 3

b)

Your matrix

Find the pivot in the 1st column in the 1st row

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by -4

Eliminate the 2nd column

solution

The system is inconsistent

	X1	X2	b
1	1	5	7
2	-2	-7	-5