Question

Write the system of linear equations, obtained in (i) above, in matrix form \( AX = B \).

Hint:

To convert a system of linear equations into matrix form: 1. Write the coefficients of variables in a matrix \( A \). 2. Write the variables in a column matrix \( X \) and the constants in \( B \).

Answer 1

The system of linear equations: \[ 10x - 8y = 80, \quad -10x + 16y = 160. \]
Matrix form \( AX = B \): \[ A = \begin{bmatrix} 10 & -8 \\ -10 & 16 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \end{bmatrix}, \quad B = \begin{bmatrix} 80 \\ 160 \end{bmatrix}. \]
Thus, \[ AX = B \quad \text{is written as:} \quad \begin{bmatrix} 10 & -8 \\ -10 & 16 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 80 \\ 160 \end{bmatrix}. \]