1. The problem is to multiply the scalar 5 by the matrix \(\begin{bmatrix}a & b \\ c & d\end{bmatrix}\). 2. The formula for scalar multiplication of a matrix is: $$k \times \begin{bmatrix}x_{11} & x_{12} \\ x_{21} & x_{22}\end{bmatrix} = \begin{bmatrix}k x_{11} & k x_{12} \\ k x_{21} & k x_{22}\end{bmatrix}$$ where \(k\) is the scalar. 3. Applying this to our problem: $$5 \times \begin{bmatrix}a & b \\ c & d\end{bmatrix} = \begin{bmatrix}5a & 5b \\ 5c & 5d\end{bmatrix}$$ 4. This means each element of the matrix is multiplied by 5. 5. The final answer is: $$\begin{bmatrix}5a & 5b \\ 5c & 5d\end{bmatrix}$$