Final answer:
A system of equations is written in matrix form by organizing the coefficients into a matrix (A), the variables into a vector (X), and the constants into another vector (B), and expressing it as AX = B.
Step-by-step explanation:
To write a system of equations in matrix form, you begin by organizing the coefficients of the variables into a matrix, the variables into a vector, and the constants into another vector. Let's consider a system of linear equations as an example:
To express this system in matrix form, we write it as AX = B where A is the coefficient matrix, X is the variable vector, and B is the constant vector.
The matrix A would consist of the coefficients of x and y:
A = | 2 3 |
| -1 4 |
The variable vector X would be:
X = | x |
| y |
And the constant vector B would be:
B = | 5 |
| 6 |
Therefore, the matrix form of the system of equations would be:
| 2 3 | | x | | 5 |
| -1 4 | | y | = | 6 |
This compact representation makes it easier to apply matrix operations to solve the system of equations.