Mathematics · University
Determinant of a 3 × 3 triangular matrix
Off-diagonal entries do not enter this special-case determinant; this is not true for every matrix.
Method and conditions
Off-diagonal entries do not enter this special-case determinant; this is not true for every matrix.
det A = product of diagonal entries (triangular A)
Worked examples
Find det A for A = [[-2,6,6],[0,4,12],[0,0,5]]. Round the final result to 4 decimal places if needed.
A is upper triangular, so det A = (-2)(4)(5).
-40
Find det A for A = [[3,6,10],[0,3,16],[0,0,2]]. Round the final result to 4 decimal places if needed.
A is upper triangular, so det A = (3)(3)(2).
18
Try it
Find det A for A = [[-6,9,7],[0,-1,16],[0,0,7]]. Round the final result to 4 decimal places if needed.
Find det A for A = [[-7,1,8],[0,-8,9],[0,0,9]]. Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 42
A is upper triangular, so det A = (-6)(-1)(7).
- 504
A is upper triangular, so det A = (-7)(-8)(9).
Further reading and review references
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