### Instruction: Compute $\begin{pmatrix} 1 & 2 \\ 4 & 8 \\ \end{pmatrix} \begin{pmatrix} 5 \\ 3 \end{pmatrix}.$.### Response: To multiply a matrix by a vector, I need to make sure the number of columns in the matrix matches the number of rows in the vector.
In this case, they both have 2, so I can proceed.
The result will be another vector with the same number of rows as the matrix, which is 2.
To find each entry of the result, I need to multiply the corresponding row of the matrix by the vector and add up the products.
For the first entry of the result, I multiply the first row of the matrix, (1, 2), by the vector, (5, 3), and add up the products.
That gives me 1 * 5 + 2 * 3 = 5 + 6 = 11.
For the second entry of the result, I multiply the second row of the matrix, (4, 8), by the vector, (5, 3), and add up the products.
That gives me 4 * 5 + 8 * 3 = 20 + 24 = 44.
Therefore, the result is the vector (11, 44).