Math Problem Statement
- 7x+3y=21 x+3y=33 ket: x+y = 2, selesaikan dengan pldv matriks
Solution
To solve the system of equations using the method of matrices (PLDV), we can express the equations in matrix form:
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The original equations are:
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Rewrite in matrix form :
7 & 3 \\ 1 & 3 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 21 \\ 33 \end{bmatrix}$$ -
Let , , and .
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Calculate the inverse of matrix :
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The determinant of is:
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The inverse is given by:
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Now, multiply with :
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Calculating :
Now divide by 18:
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Therefore, the solution is:
If you need further details or have any questions about the process, let me know!
Related Questions:
- What would the solution be if the second equation were changed?
- How can you verify the solution graphically?
- What happens if the determinant of matrix is zero?
- Can you explain how to find the inverse of a matrix in general?
- How can you apply this method to a system of three equations?
Tip:
Always check the solution by substituting back into the original equations to ensure accuracy.
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Systems of Equations
Matrix Inversion
Formulas
AX = B
X = A^{-1}B
det(A)
Theorems
Inverse Matrix Theorem
Suitable Grade Level
Grades 10-12
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