Matrix Form A6D457
1. The problem is to express a system or equation in matrix form.
2. The matrix form of a system of linear equations is generally written as $$AX = B$$ where:
- $$A$$ is the coefficient matrix,
- $$X$$ is the column matrix of variables,
- $$B$$ is the column matrix of constants.
3. For example, if the system is:
$$\begin{cases} a_{11}x_1 + a_{12}x_2 + \cdots + a_{1n}x_n = b_1 \\ a_{21}x_1 + a_{22}x_2 + \cdots + a_{2n}x_n = b_2 \\ \vdots \\ a_{m1}x_1 + a_{m2}x_2 + \cdots + a_{mn}x_n = b_m \end{cases}$$
then the matrix form is:
$$\begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix} = \begin{bmatrix} b_1 \\ b_2 \\ \vdots \\ b_m \end{bmatrix}$$
4. This form helps to solve the system using matrix operations like inversion or row reduction.
5. If you provide a specific system, I can write it explicitly in matrix form for you.