Numerical Method Please provide whole process of solution Th

Numerical Method

Please provide whole process of solution. Thanks!!!!

The following problem is to be worked by hand and will require use of a calculator such as a TI-83/TI-84. Do not use a MATLAB script to find a solution. For the following system of equations Ax = b solve by using Gauss-Jordan elimination with pivoting using a calculator that employs four decimal digit floating point arithmetic. A = [1 1/2 1/3 1/4 1/2 1/3 1/4 1/5 1/3 1/4 1/5 1/6 1/4 1/5 1/6 1/7], b = [1 -1 1 -1], x = [ 516 -5700 13620 -8820]

Solution

By matrix: Ax=b

        and by gauss jordan floating point arithmetic method

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

Multiply the 1st row by 1/2

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

Multiply the 1st row by 1/3

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

Multiply the 1st row by 1/4

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

Make the pivot in the 2nd column by dividing the 2nd row by 1/12

Multiply the 2nd row by 1/2

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

Multiply the 2nd row by 1/12

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

Multiply the 2nd row by 3/40

Subtract the 2nd row from the 4th row and restore it

Make the pivot in the 3rd column by dividing the 3rd row by 1/180

Multiply the 3rd row by -1/6

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

Subtract the 3rd row from the 2nd

Multiply the 3rd row by 1/120

Subtract the 3rd row from the 4th row and restore it

Make the pivot in the 4th column by dividing the 4th row by 1/2800

Multiply the 4th row by 1/20

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

Multiply the 4th row by -3/5

Subtract the 4th row from the 2nd row and restore it

Multiply the 4th row by 3/2

Subtract the 4th row from the 3rd row and restore it

Solution set:

x1 = 516

x2 = -5700

x3 = 13620

x4 = -8820

	X1	X2	X3	X4	b
1	1	1/2	1/3	1/4	1
2	1/2	1/3	1/4	1/5	-1
3	1/3	1/4	1/5	1/6	1
4	1/4	1/5	1/6	1/7	-1