Numerical Method Please provide whole process of solution. Thanks!!!! The follow
ID: 3421238 • Letter: N
Question
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]Explanation / Answer
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 -1Related Questions
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