The problem requires us to multiply a $2 \times 1$ matrix with a $2 \times 2$ matrix: $\begin{bmatrix} 5 \\ \frac{1}{4} \end{bmatrix} \begin{bmatrix} 4 & 3 \\ 16 & 0 \end{bmatrix}$

1. Problem Description

The problem requires us to multiply a $2 \times 1$ matrix with a $2 \times 2$ matrix:

$\begin{bmatrix} 5 \\ \frac{1}{4} \end{bmatrix} \begin{bmatrix} 4 & 3 \\ 16 & 0 \end{bmatrix}$

2. Solution Steps

The resulting matrix will be a $2 \times 2$ matrix. We calculate the elements as follows:

$(1,1)$ element: $(5)(4) + (\frac{1}{4})(16) = 20 + 4 = 24$

$(1,2)$ element: $(5)(3) + (\frac{1}{4})(0) = 15 + 0 = 15$

Therefore, the resulting matrix is:

$\begin{bmatrix} 24 & 15 \end{bmatrix}$

3. Final Answer

$\begin{bmatrix} 24 & 15 \end{bmatrix}$