To complete the table with the given values, we need to determine the missing entries in the table. Here’s the detailed step-by-step process on how to fill in the missing values:
1. Identify the Given Data:
- The given table contains some known values and some blanks.
- We are given a table that looks like this:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 \\
\hline
1 & 1 & 2 & 3 & 4 \\
\hline
2 & 2 & \quad & 1 & 3 \\
\hline
3 & 3 & 1 & \quad & 2 \\
\hline
4 & 4 & 3 & 2 & \quad \\
\hline
\end{array}
\][/tex]
2. Analyze the Pattern in the Table:
- This table seems to be a multiplication table for the values 1, 2, 3, and 4.
- The first row and first column contain the multiplication factors.
3. Fill in the Missing Values for Row 2:
- The multiplication of 2 and 2 is [tex]\(2 \times 2 = 4\)[/tex].
- So, the missing value in the second row and second column (2, 2) is 4.
4. Fill in the Missing Values for Row 3:
- The multiplication of 3 and 3 is [tex]\(3 \times 3 = 9\)[/tex].
- So, the missing value in the third row and third column (3, 3) is 9.
5. Fill in the Missing Values for Row 4:
- The multiplication of 4 and 4 is [tex]\(4 \times 4 = 16\)[/tex].
- So, the missing value in the fourth row and fourth column (4, 4) is 16.
6. Complete the Table:
- Now we fill in all the identified missing values into the table. The completed table looks like this:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 \\
\hline
1 & 1 & 2 & 3 & 4 \\
\hline
2 & 2 & 4 & 1 & 3 \\
\hline
3 & 3 & 1 & 9 & 2 \\
\hline
4 & 4 & 3 & 2 & 16 \\
\hline
\end{array}
\][/tex]
Therefore, Table 1 completed looks as follows:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 \\
\hline
1 & 1 & 2 & 3 & 4 \\
\hline
2 & 2 & 4 & 1 & 3 \\
\hline
3 & 3 & 1 & 9 & 2 \\
\hline
4 & 4 & 3 & 2 & 16 \\
\hline
\end{array}
\][/tex]
