Math Problem Statement
10a+5b= -680.3938 4.5a+18b+4.5c=-957.906 4.5b+18c+4.5d=-957.906 4.5c+18d+4.5e=-957.906 4.5d+18e+4.5f=-957.906 4.5e+9f=-478.953
Find the unknown variables.
Solution
You have a system of 6 equations with 6 unknowns, which can be solved using substitution, elimination, or matrix methods. Let's summarize the system for clarity:
The most efficient way to solve this system is to use matrix methods (Gaussian elimination or matrix inverses). I'll use a direct approach to solve for all unknown variables.
Let me calculate the solution for you. numpy as np
Coefficients matrix
A = np.array([ [10, 5, 0, 0, 0, 0], [4.5, 18, 4.5, 0, 0, 0], [0, 4.5, 18, 4.5, 0, 0], [0, 0, 4.5, 18, 4.5, 0], [0, 0, 0, 4.5, 18, 4.5], [0, 0, 0, 0, 4.5, 9] ])
Constants vector
B = np.array([-680.3938, -957.906, -957.906, -957.906, -957.906, -478.953])
Solving the system of equations
solution = np.linalg.solve(A, B) solutionThe solution to the system of equations is as follows:
These are the values of the unknown variables.
Would you like more details or an explanation of the solution process? Also, here are some related questions you might find interesting:
- How can you check the solution of a system of equations?
- What is Gaussian elimination and how does it relate to solving systems of linear equations?
- How do matrix inverses help in solving linear systems?
- Can this system be solved using substitution or elimination methods?
- What are the advantages of using numerical methods for solving systems of equations?
Tip: In practice, always verify the solution by substituting the values back into the original equations to confirm they satisfy all of them.
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Systems of Linear Equations
Matrix Methods
Formulas
Ax = B (Matrix equation)
Gaussian elimination
Matrix inverse method
Theorems
Cramer's Rule
Gaussian Elimination
Inverse Matrix Theorem
Suitable Grade Level
Grades 11-12
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