Exercise · ZW-DETERMINANT-003 · ★☆☆ Basic
Compute the determinant of the upper triangular matrix \(\begin{pmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 6\end{pmatrix}\).
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- D. \(24\)
Explanation
For a triangular matrix the determinant is the product of the diagonal entries: \(1\cdot4\cdot6=24\). The sum of the diagonal (15) is the trace, not the determinant.
Review the concept: Determinant
The determinant of a square matrix is a number that measures how much the linear transformation it defines scales volumes.
\[\det\begin{pmatrix}a&b\\c&d\end{pmatrix}=ad-bc\]
More practice problems: determinant
- ZW-DETERMINANT-001 Compute det A for A=[3 1; 2 4].
- ZW-DETERMINANT-002 Compute the determinant of [2 -1; 5 3].
- ZW-DETERMINANT-004 For which value of k is det[k 2; 3 6]=0?
- ZW-DETERMINANT-005 What is the determinant of the identity matrix I_3?
- ZW-DETERMINANT-006 Compute det A using the rule of Sarrus for A=[2 0 1; 1 3 2; 0 1 4].
- ZW-DETERMINANT-007 The parallelogram spanned by the vectors (3,1) and (1,2) has area:
- ZW-DETERMINANT-008 Find all values of x such that det[x 1; 4 x]=0.
- ZW-DETERMINANT-009 Let A be a 2×2 matrix with det A=7. What is det(2A)?