Answer :
Let's fill in the above table step-by-step based on the row and column headers provided.
Given table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & & & & \\ \hline \text{2} & & & & \\ \hline \text{2} & & & & \\ \hline \text{21} & & & & \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
To fill in the table, let's compute the product of each row header and each column header.
First Row (Row header = 3):
1. First Column: [tex]\(3 \times 2 = 6\)[/tex]
2. Second Column: [tex]\(3 \times 3 = 9\)[/tex]
3. Third Column (no column header, use row header): [tex]\(3\)[/tex]
4. Fourth Column: [tex]\(3 \times 2 = 6\)[/tex]
Updated table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & & & & \\ \hline \text{2} & & & & \\ \hline \text{21} & & & & \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
Second Row (Row header = 2):
1. First Column: [tex]\(2 \times 2 = 4\)[/tex]
2. Second Column: [tex]\(2 \times 3 = 6\)[/tex]
3. Third Column (no column header, use row header): [tex]\(2\)[/tex]
4. Fourth Column: [tex]\(2 \times 2 = 4\)[/tex]
Updated table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{2} & & & & \\ \hline \text{21} & & & & \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
Third Row (Row header = 2):
1. First Column: [tex]\(2 \times 2 = 4\)[/tex]
2. Second Column: [tex]\(2 \times 3 = 6\)[/tex]
3. Third Column (no column header, use row header): [tex]\(2\)[/tex]
4. Fourth Column: [tex]\(2 \times 2 = 4\)[/tex]
Updated table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{21} & & & & \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
Fourth Row (Row header = 21):
1. First Column: [tex]\(21 \times 2 = 42\)[/tex]
2. Second Column: [tex]\(21 \times 3 = 63\)[/tex]
3. Third Column (no column header, use row header): [tex]\(21\)[/tex]
4. Fourth Column: [tex]\(21 \times 2 = 42\)[/tex]
Updated table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{21} & 42 & 63 & 21 & 42 \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
Fifth Row (Row header = 12):
1. First Column: [tex]\(12 \times 2 = 24\)[/tex]
2. Second Column: [tex]\(12 \times 3 = 36\)[/tex]
3. Third Column (no column header, use row header): [tex]\(12\)[/tex]
4. Fourth Column: [tex]\(12 \times 2 = 24\)[/tex]
Final filled-in table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{21} & 42 & 63 & 21 & 42 \\ \hline \text{12} & 24 & 36 & 12 & 24 \\ \hline \end{tabular} \][/tex]
All entries are now filled correctly according to the given row and column headers.
Given table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & & & & \\ \hline \text{2} & & & & \\ \hline \text{2} & & & & \\ \hline \text{21} & & & & \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
To fill in the table, let's compute the product of each row header and each column header.
First Row (Row header = 3):
1. First Column: [tex]\(3 \times 2 = 6\)[/tex]
2. Second Column: [tex]\(3 \times 3 = 9\)[/tex]
3. Third Column (no column header, use row header): [tex]\(3\)[/tex]
4. Fourth Column: [tex]\(3 \times 2 = 6\)[/tex]
Updated table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & & & & \\ \hline \text{2} & & & & \\ \hline \text{21} & & & & \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
Second Row (Row header = 2):
1. First Column: [tex]\(2 \times 2 = 4\)[/tex]
2. Second Column: [tex]\(2 \times 3 = 6\)[/tex]
3. Third Column (no column header, use row header): [tex]\(2\)[/tex]
4. Fourth Column: [tex]\(2 \times 2 = 4\)[/tex]
Updated table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{2} & & & & \\ \hline \text{21} & & & & \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
Third Row (Row header = 2):
1. First Column: [tex]\(2 \times 2 = 4\)[/tex]
2. Second Column: [tex]\(2 \times 3 = 6\)[/tex]
3. Third Column (no column header, use row header): [tex]\(2\)[/tex]
4. Fourth Column: [tex]\(2 \times 2 = 4\)[/tex]
Updated table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{21} & & & & \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
Fourth Row (Row header = 21):
1. First Column: [tex]\(21 \times 2 = 42\)[/tex]
2. Second Column: [tex]\(21 \times 3 = 63\)[/tex]
3. Third Column (no column header, use row header): [tex]\(21\)[/tex]
4. Fourth Column: [tex]\(21 \times 2 = 42\)[/tex]
Updated table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{21} & 42 & 63 & 21 & 42 \\ \hline \text{12} & & & & \\ \hline \end{tabular} \][/tex]
Fifth Row (Row header = 12):
1. First Column: [tex]\(12 \times 2 = 24\)[/tex]
2. Second Column: [tex]\(12 \times 3 = 36\)[/tex]
3. Third Column (no column header, use row header): [tex]\(12\)[/tex]
4. Fourth Column: [tex]\(12 \times 2 = 24\)[/tex]
Final filled-in table:
[tex]\[ \begin{tabular}{|c|c|c|c|c|} \hline & \text{2} & \text{3} & & \text{2} \\ \hline \text{3} & 6 & 9 & 3 & 6 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{2} & 4 & 6 & 2 & 4 \\ \hline \text{21} & 42 & 63 & 21 & 42 \\ \hline \text{12} & 24 & 36 & 12 & 24 \\ \hline \end{tabular} \][/tex]
All entries are now filled correctly according to the given row and column headers.
