Question

question 1 - 1
a matrix equation is shown
\\(\

$$\begin{bmatrix}4& - 8&0\\3&1&2\\ - 7&0&4\\end{bmatrix}$$

\times\

$$\begin{bmatrix}5&3&0\\ - 2&8&7\\3& - 1&5\\end{bmatrix}$$

=\

$$\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\\end{bmatrix}$$

\\)
enter the value of (a_{11}) in the box
(a_{11}=)

Explanation:

Step1: Recall matrix - multiplication rule

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

$$\begin{bmatrix}4& - 8&0\end{bmatrix}$$

\) and the first column of the second matrix \(

$$\begin{bmatrix}0\\-2\\3\end{bmatrix}$$

\).

Step2: Calculate the dot - product

\(a_{11}=(4\times0)+(-8\times(-2))+(0\times3)\)
\(a_{11}=0 + 16+0\)

Answer:

\(16\)