Solve the following system of equations by using Matrix &

Question

Solve the following system of equations by using Matrix Inverse Method.
1. 3x+ 4y+ 7z= 14
2. 2x-y+ 3z= 4
3. 2x + 2y - 3z = 0

27 Apr 2023

Answer :

Word Count : 912

To solve the given system of equations using the Matrix Inverse Method, we need to represent the system in matrix form and find the inverse of the coefficient matrix. Let's proceed with the steps:

Step 1: Write the system of equations in matrix form:
| 3 4 7 | | x | | 14 |
| 2 -1 3 | * | y | = | 4 |
| 2 2 -3 | | z | | 0 |

Step 2: Define the coefficient matrix A, the variable matrix X, and the constant matrix B:
A = | 3 4 7 |
| 2 -1 3 |
| 2 2 -3 |

X = | x |
| y |
| z |

B = | 14 |
| 4 |
| 0 |
Step 3: Calculate the inverse of matrix A:
A_inv = A^(-1)

Step 4: Multiply both sides of the equation by A_inv:
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