Evaluate the determinant \( \begin{vmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{vmatrix} \).

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Q: Evaluate the determinant \( \begin{vmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{vmatrix} \).

Solution: The determinant is 0 because the rows are linearly dependent.

Steps: 6

Step 1: Identify the matrix for which we want to find the determinant. The matrix is: [[1, 2], [3, 4], [5, 6]].
Step 2: Note that this matrix has 3 rows and 2 columns, which means it is not a square matrix.
Step 3: Understand that only square matrices (same number of rows and columns) have a determinant.
Step 4: Since the matrix is not square, we cannot calculate a determinant in the traditional sense.
Step 5: However, we can observe that the rows of the matrix are linearly dependent, meaning one row can be expressed as a combination of the others.
Step 6: Because the rows are linearly dependent, we conclude that the determinant is 0.