Use Gauss-Jordan row reduction to solve the given system of equations. 9x−10y =9 36x−40y=36

Falak Kinney 2021-02-09 Answered
Use Gauss-Jordan row reduction to solve the given system of equations.
9x−10y =9
36x−40y=36
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Expert Answer

grbavit
Answered 2021-02-10 Author has 109 answers
Step 1
The objective is to find a solution for the given system of equations using Gauss-Jordan elimination method.
The system of equations given is
9x−10y =9
36x−40y=36
The matrix representation of the above system of equations is
[9103640][xy]=[936],AX=B.
Then the augmented matrix [AB] becomes
[9109364036]
Step 2
Now, reducing the matrix [AB] step-by-step,(Gauss Jordan row reduction),
R214R2 The matrix [AB] becomes [91099109]
R2R2R1 The matrix [AB] becomes [9109000]
The reduced matrix can be expressed as 9x+10y = 9.
Let y = k, any arbitrary value, the x=910k9
This system has infinitely many solutions.
(x,y)=(910k9,k)
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