Linear Algebra System of Equations

Matrices and Linear Equations

• The system of linear equations is represented as: $5x + 3y = -1$ and $2x + y = -8$
• The above system can be represented in matrix form as: $\begin{bmatrix} 5 & 3 \ 2 & 1\end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} -1 \ -8 \end{bmatrix}$
• The matrix equation can be written in compact form as: $\frac{\begin{bmatrix} 5 & 3 \ 2 & 1 \end{bmatrix}}{A} \frac{\begin{bmatrix} x \ y \end{bmatrix}}{x} = \frac{\begin{bmatrix} -1 \ -8 \end{bmatrix}}{B}$
• The determinant of matrix A is: $|A| = \begin{vmatrix} 5 & 3 \ 2 & 1 \end{vmatrix} = -1$
• The determinant of matrix A for x is: $d(A) = \begin{vmatrix} 5 & -3 \ 2 & 1 \end{vmatrix} = 11$