What is the value of \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \

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Question: What is the value of \\( \\begin{vmatrix} 1 & 1 & 1 \\\\ 1 & 2 & 3 \\\\ 1 & 3 & 6 \\end{vmatrix} \\)?

Options:

Correct Answer: 0

Solution:

The determinant is 0 because the first column is repeated.

What is the value of \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?

What is the value of \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \)?

Step 1: Identify the matrix given in the question: \( \begin{vmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \end{vmatrix} \).
Step 2: Look at the first column of the matrix. It has the values 1, 1, and 1.
Step 3: Notice that the first column is repeated in the sense that all the entries are the same (1).
Step 4: Recall the property of determinants: if any two columns (or rows) of a matrix are identical or proportional, the determinant is 0.
Step 5: Since the first column is repeated (all entries are 1), we conclude that the determinant is 0.

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