Use Cramers Rule to solve the following system of equations

Use Cramer\'s Rule to solve the following system of equations: 3y + 4z = 14.8 4x + 2y - z = -6.3 x - y + 5z = 13.5 Use Gauss-Jordan Elimination to solve the system of equations in #5.

Solution

cramers rule

Your matrix

Write down the main matrix and find its determinant

D = -87

Very detailed solution  

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

D1 = 104.4

Very detailed solution  

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

D2 = -69.60000000000004

Very detailed solution  

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

D3 = -269.70000000000005

Very detailed solution  

x1 = D1 / D = 104.4 / (-87) = -1.2

x2 = D2 / D = -69.60000000000004 / (-87) = 0.8000000000000004

x3 = D3 / D = -269.70000000000005 / (-87) = 3.1000000000000005

Solution set:

x1 = -1.2

x2 = 0.8000000000000004

x3 = 3.1000000000000005

2. guass jordan

Your matrix

Find the pivot in the 1st column and swap the 3rd and the 1st rows

Eliminate the 1st column

Make the pivot in the 2nd column by dividing the 2nd row by 6

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 14.5

Eliminate the 3rd column

Solution set:

x1 = -1.1999999999999993

x2 = 0.8000000000000007

x3 = 3.1

	X1	X2	X3	b
1	0	3	4	14.8
2	4	2	-1	-6.3
3	1	-1	5	13.5