To solve for the missing values in the matrix, we need to determine the overall sum of each row to ensure consistency with the given values. Let’s examine each row step by step:
1. First Row:
[tex]\[
12 + 18 = 30
\][/tex]
To achieve 28 in the third column of the first row:
[tex]\[
12 + 18 + \text{(missing value)} = 28
\][/tex]
Solving for the missing value:
[tex]\[
\text{missing value} = 28 - 30 = -2
\][/tex]
The first row thus becomes:
[tex]\[
12, 18, -2, 28
\][/tex]
2. Second Row:
The value for the second row is already balanced and complete:
[tex]\[
60 + 65 + \text{(missing value)} = 35
\][/tex]
However, since the second column totals internally to 125:
[tex]\[
\text{No missing value in the second row that affects summation.}
\][/tex]
We can ignore balancing here.
3. Third Row:
We need to determine the missing value in the second column to complete the rows summing to 35:
[tex]\[
37 + \text{(missing value in column 2)} + 5 = 35
\][/tex]
Solving for the missing value in column 2:
[tex]\[
\text{missing value in column 2} = 35 - 42 = -7
\][/tex]
Synthesizing the resulting table with the missing values determined:
[tex]\[
\begin{tabular}{|l|l|l|}
\hline 12 & 18 & 28 (-2) \\
\hline 60 & 65 & 35 \\
\hline 37 & -7 (2) & 5 \\
\hline
\end{tabular}
\][/tex]
The missing values identified are [tex]\(-2\)[/tex] and [tex]\(2\)[/tex].
