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The system of equations 3x + 4y = 5, 6x + 7y = -8 is written in matrix from as |
$\left[\begin{array}{ll}3 & 4 \\ 6 & 7\end{array}\right]\left[\begin{array}{ll}x & y\end{array}\right]=\left[\begin{array}{ll}5 & -8\end{array}\right]$ $\left[\begin{array}{ll}3 & 6 \\ 4 & 7\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}5 \\ -8\end{array}\right]$ $\begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$ $\left[\begin{array}{ll}x & y\end{array}\right]\left[\begin{array}{ll}3 & 6 \\ 4 & 7\end{array}\right]=\left[\begin{array}{ll}5 & -8\end{array}\right]$ |
$\begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$ |
The correct answer is Option 3: $\begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$ Let the system be: $\begin{cases} 3x + 4y = 5 \\ 6x + 7y = -8 \end{cases}$ Matrix form A system of linear equations can be written as: $AX = B$ where $A = \begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \end{bmatrix}, \quad B = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$ Hence, the matrix form is: $\begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$ |
