Question

1. $2quad 5quad 0\begin{bmatrix}8&1\\0&4\\2&5end{bmatrix}$

Explanation:

Step1: Recall matrix multiplication rule

For a row vector \(\mathbf{A} = [a_1\ a_2\ a_3]\) and a matrix \(\mathbf{B}=

$$\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\\b_{31}&b_{32}\end{bmatrix}$$

\), the product \(\mathbf{A}\mathbf{B}\) is a row vector \([a_1b_{11} + a_2b_{21}+a_3b_{31}\ \ a_1b_{12} + a_2b_{22}+a_3b_{32}]\).

Here, \(\mathbf{A} = [2\ 5\ 0]\) and \(\mathbf{B}=

$$\begin{bmatrix}8&1\\0&4\\2&5\end{bmatrix}$$

\).

Step2: Calculate the first element of the product

First element: \(2\times8 + 5\times0+0\times2=16 + 0+0 = 16\).

Step3: Calculate the second element of the product

Second element: \(2\times1 + 5\times4+0\times5=2 + 20+0 = 22\).

Answer:

\([16\ 22]\)