Solution: The determinant is 0 because the first column is a linear combination of the others.
Steps: 9
Step 1: Identify the matrix C, which is given as C = [[1, 1, 1], [1, 2, 3], [1, 3, 6]].
Step 2: Understand that we need to find the determinant of the matrix C, denoted as |C|.
Step 3: Recall that a determinant can be calculated using various methods, but we will check for linear combinations first.
Step 4: Look at the first column of the matrix, which is [1, 1, 1].
Step 5: Notice that the first column can be expressed as a combination of the second and third columns. Specifically, if we take the second column [1, 2, 3] and subtract the first column [1, 1, 1], we get [0, 1, 2].
Step 6: Similarly, if we take the third column [1, 3, 6] and subtract twice the first column [1, 1, 1], we get [0, 1, 4].
Step 7: Since the first column can be formed from the other two columns, the columns of the matrix are linearly dependent.
Step 8: When the columns of a matrix are linearly dependent, the determinant of the matrix is 0.
