Question

question 1-1
a matrix equation is shown.
\begin{bmatrix} 4& - 5&0\\3&1&2\\7&6&4 end{bmatrix}\times\begin{bmatrix} 9&-3&6\\-2&8&7\\3&-1&5 end{bmatrix}=\begin{bmatrix} a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33} end{bmatrix}
enter the value of (a_{11}) in the box.

Explanation:

Step1: Recall matrix - multiplication rule

To find the element \(a_{11}\) of the product matrix, we take the dot - product of the first row of the first matrix and the first column of the second matrix.

Step2: Calculate the dot - product

The first row of the first matrix is \([4,-5,0]\) and the first column of the second matrix is \(

$$\begin{bmatrix}9\\-2\\3\end{bmatrix}$$

\). The dot - product is \(4\times9+( - 5)\times(-2)+0\times3\).
\[

$$\begin{align*} a_{11}&=4\times9+( - 5)\times(-2)+0\times3\\ &=36 + 10+0\\ &=46 \end{align*}$$

\]

Answer:

46