Question

find the product of the two matrices
8 6 5×\

$$\begin{bmatrix}4 \\\\ 2 \\\\ 7\\end{bmatrix}$$

79
1292
11245
369355

Explanation:

Step1: Recall matrix - multiplication rule

For a $1\times3$ matrix

$$\begin{bmatrix}a&b&c\end{bmatrix}$$

and a $3\times1$ matrix

$$\begin{bmatrix}d\\e\\f\end{bmatrix}$$

, the product is a $1\times1$ matrix given by $ad + be+cf$.
Here, $a = 8$, $b = 6$, $c = 5$, $d = 4$, $e = 2$, $f = 7$.

Step2: Calculate the product

\[

$$\begin{align*} &8\times4+6\times2 + 5\times7\\ =&32+12 + 35\\ =&44+35\\ =&79 \end{align*}$$

\]
The product matrix is

$$\begin{bmatrix}79\end{bmatrix}$$

.

Answer:

$$\begin{bmatrix}79\end{bmatrix}$$