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Solving Systems of Linear Equations using Matrix Algebra (AX=B)
Published on March 11, 2026
Linear-Algebra
Demonstrates how to convert a simultaneous equation set into the matrix equation AX=B and solve it using techniques like matrix inversion or augmented matrix reduction.
Question
SYSTEM OF EQUATION IN MATRIX TO SOLVE SIMULTANEOUS EQUATION
Answer
This is a general request. To solve a system of linear equations using matrices, you need to provide the specific system of equations you want to solve.
A system of
where:
-
is the coefficient matrix. -
is the column vector of variables. -
is the column vector of constants.
To solve for
Alternatively, the system can be solved using Gaussian elimination or Gauss-Jordan elimination on the augmented matrix
Please provide the specific system of simultaneous equations you wish to solve.
Example (Illustrative Solution Steps):
Suppose you have the following system:
-
Write in Matrix Form (
): -
Method 1: Using Inverse (
) - Calculate the determinant of
: . - Calculate the inverse
: - Calculate
: - Therefore,
and .
- Calculate the determinant of
-
Method 2: Using Augmented Matrix and Gaussian Elimination
- Set up the augmented matrix:
- Swap
and : - Perform
: - Perform
: - Perform
(Gauss-Jordan): - The solution is
and .
- Set up the augmented matrix:
Please provide your specific equations so I can solve them step-by-step.