Which of the following upper triangular matrices has a determinant equal to 16.
A) matrix D
B) matrix B
C) matrix A
D) matrix C
E) matrix E

Question

Which of the following  upper triangular matrices has a determinant equal to 16.     
A) matrix D 
B) matrix B 
C) matrix A 
D) matrix C 
E) matrix E

Quizplus · Accepted Answer

Using the formula for the determinant of an upper triangular matrix, we see that the determinant is simply the product of the entries on the diagonal. Therefore, in order for the determinant to be equal to 16, we need the product of the diagonal entries to be 16.

The diagonal entries of matrix A are 2, 2, and 4, which means the determinant is 2*2*4 = 16. Therefore, matrix A is the only matrix that satisfies the given condition.

Which of the Following Upper Triangular Matrices Has a Determinant