If C = [[1, 0, 2], [0, 1, 3], [0, 0, 1]], what is det(C)? (2019)

If C = [[1, 0, 2], [0, 1, 3], [0, 0, 1]], what is det(C)? (2019)

Step 1: Identify the matrix C, which is given as C = [[1, 0, 2], [0, 1, 3], [0, 0, 1]].
Step 2: Recognize that C is an upper triangular matrix. This means all the elements below the main diagonal are zero.
Step 3: Find the diagonal elements of the matrix C. The diagonal elements are 1 (from the first row), 1 (from the second row), and 1 (from the third row).
Step 4: Calculate the product of the diagonal elements. Multiply 1 * 1 * 1.
Step 5: The result of the multiplication is 1, which is the determinant of the matrix C.

Determinant of a Matrix – The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties about the matrix, such as whether it is invertible.
Upper Triangular Matrix – An upper triangular matrix is a type of square matrix where all the entries below the main diagonal are zero. The determinant of such a matrix is the product of its diagonal elements.