Using Gauss elimination solve following simultaneous equation 2x-6y+8z = 24, 5x+4y-3z = 2, 3x+y+2z = 16
Answers
Step-by-step explanation:
(3x2=6)
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Do you think that Richard's mother and teacher Richard E. Weiherer were instrumental in
making him a worthy scientist'? Why, why not?
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Solution
In mathematics, the Gaussian elimination method is known as a row reduction algorithm for solving systems of linear equations. It consists of a sequence of operations performed on the corresponding matrix of coefficients.
The steps of the Gaussian elimination method are
(1) Write the given system of linear equations in the matrix form AX = B, where A is the matrix of coefficients, X is the column matrix of unknowns, and B is the column matrix of constants.
(2) Reduce the augmented matrix [A : B] by elementary row operations to obtain [A' : B'].
(3) We get A' as an upper triangular matrix.
(4) By back substitution in A'X = B' we get the solution of the given system of linear equations.
Given
2x-6y+8z = 24, 5x+4y-3z = 2, 3x+y+2z = 16 equations are given
Find
We need to find the value of x,y,z
Solution
2 -6 8 | 24
5 4 -3 | 2
3 1 2 | 16
R3→R3 -(3/2)R1 and R2→R2-(5/2)R1
2 -6 8 | 24
0 19 -23 | -58
0 10 -10 | -20
R3→R3/10 and R1→R1/2
1 -3 4 | 12
0 19 -23 | -58
0 1 -1 | -2
R3→R3-(1/19)R2
1 -3 4 | 12
0 19 -23 | -58
0 0 4/19 | 20/19
4/19z= 20/19 → 4z=20 → z=20/4 =5
19y-23z= -58
Put z=5 in this equation,we get
19y-23(5)= -58
19y= -58+115
19y=57
y=57/19=3
y=3
x-3y+4z=12
put value of y and z in this equation,we get
x-3(3)+4(5)=12
x-9+20=12
x=1
Hence the value of x=1,y=3 and z=5
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