Subjects linear algebra

Matrix Form A6D457

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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.