Find the determinant of A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]].
Solution
Problem
Find the determinant of A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]].
Step 1: Identify the structure of the matrix.
A = [[1, 2, 3], [0, 4, 5], [0, 0, 6]]
This is an upper triangular matrix because all entries below the main diagonal are zero.
Step 2: Recall the determinant rule for triangular matrices.
The determinant of a triangular matrix is the product of its diagonal entries.
The diagonal entries are 1, 4, and 6.
Step 3: Multiply the diagonal entries.
det(A) = (1)(4)(6)
det(A) = 24
Therefore, the determinant of A is 24.
Result
det(A) = 24