Solution: The determinant is 0 because the first column is a linear combination of the other columns.
Steps: 6
Step 1: Identify the matrix C, which is given as C = [[1, 1, 1], [1, 2, 3], [1, 3, 6]].
Step 2: Understand that the determinant of a matrix can be zero if one column is a linear combination of the others.
Step 3: Look at the first column of the matrix, which is [1, 1, 1].
Step 4: Check if the first column can be formed by adding or scaling the other columns.
Step 5: Notice that the first column can be expressed as a combination of the second and third columns: 1 * (second column) - 1 * (third column) = [1, 1, 1].
Step 6: Since the first column is a linear combination of the other columns, the determinant of the matrix C is 0.
