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1/16x+1/15y=9/20 , 1/20x-1/27y=4/45
? Related: Equations and Matrices (Part - 1)
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1/16x+1/15y=9/20 , 1/20x-1/27y=4/45 Related: Equations and Matrices (...
Equations and Matrices (Part - 1)
Introduction
In this topic, we will be discussing how to solve systems of linear equations using matrices. We will be using the method of elimination to reduce the system of equations to an upper triangular matrix, which can then be solved using back-substitution.
System of Equations
The given system of equations are:
1/16x + 1/15y = 9/20
1/20x - 1/27y = 4/45
Matrix Form
We can write the given system of equations in matrix form as:
AX = B
where,
A = [1/16 1/15; 1/20 -1/27]
X = [x;y]
B = [9/20; 4/45]
Augmented Matrix
We can write the augmented matrix for the given system of equations as:
[1/16 1/15 | 9/20; 1/20 -1/27 | 4/45]
Reduced Row Echelon Form
Using the method of elimination, we can reduce the augmented matrix to its reduced row echelon form:
[1 0 | 4/3; 0 1 | -2/3]
Solution
From the reduced row echelon form, we can see that:
x = 4/3
y = -2/3
Conclusion
Thus, the solution to the given system of equations is x = 4/3 and y = -2/3.
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1/16x+1/15y=9/20 , 1/20x-1/27y=4/45 Related: Equations and Matrices (Part - 1)?
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1/16x+1/15y=9/20 , 1/20x-1/27y=4/45 Related: Equations and Matrices (Part - 1)? for CA CPT 2025 is part of CA CPT preparation. The Question and answers have been prepared according to the CA CPT exam syllabus. Information about 1/16x+1/15y=9/20 , 1/20x-1/27y=4/45 Related: Equations and Matrices (Part - 1)? covers all topics & solutions for CA CPT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1/16x+1/15y=9/20 , 1/20x-1/27y=4/45 Related: Equations and Matrices (Part - 1)?.
1/16x+1/15y=9/20 , 1/20x-1/27y=4/45 Related: Equations and Matrices (Part - 1)? for CA CPT 2025 is part of CA CPT preparation. The Question and answers have been prepared according to the CA CPT exam syllabus. Information about 1/16x+1/15y=9/20 , 1/20x-1/27y=4/45 Related: Equations and Matrices (Part - 1)? covers all topics & solutions for CA CPT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1/16x+1/15y=9/20 , 1/20x-1/27y=4/45 Related: Equations and Matrices (Part - 1)?.
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