Let's analyze the given matrix and the task at hand. The given matrix is:
[tex]\[
\begin{array}{cccc}
2 & -3 & 9 & 5 \\
8 & ? & 3 & 7 \\
-4 & 2 & 4 & -6 \\
5 & 2 & 8 & 1
\end{array}
\][/tex]
The question involves finding the missing value, denoted by "?", in the second row of the matrix. To do this, let's follow a step-by-step approach.
1. Identify the row containing the missing value:
[tex]\[
8, \; ?, \; 3, \; 7
\][/tex]
2. Calculate the sum of the known elements in the row:
[tex]\[
8 + 3 + 7 = 18
\][/tex]
3. Count the number of known elements in the row:
[tex]\[
3 \; (\text{elements: } 8, \; 3, \; 7)
\][/tex]
4. Determine the average of the known elements in the row:
[tex]\[
\text{Average} = \frac{\text{Sum of known elements}}{\text{Number of known elements}} = \frac{18}{3} = 6
\][/tex]
5. The calculated average of the known elements is 6. Therefore, the missing value is 6. Update the matrix with the missing value:
[tex]\[
\begin{array}{cccc}
2 & -3 & 9 & 5 \\
8 & 6 & 3 & 7 \\
-4 & 2 & 4 & -6 \\
5 & 2 & 8 & 1
\end{array}
\][/tex]
In conclusion, the missing value in the matrix is 6, and the updated matrix is:
[tex]\[
\begin{array}{cccc}
2 & -3 & 9 & 5 \\
8 & 6 & 3 & 7 \\
-4 & 2 & 4 & -6 \\
5 & 2 & 8 & 1
\end{array}
\][/tex]
Intermediate results:
- Sum of known elements in the second row: 18
- Number of known elements: 3
- Calculated missing value: 6
