Exercise · ZW-DETERMINANT-006 · ★★☆ Intermediate
Compute \(\det A\) using the rule of Sarrus for \(A=\begin{pmatrix}2 & 0 & 1 \\ 1 & 3 & 2 \\ 0 & 1 & 4\end{pmatrix}\).
Choose one option.
Show answer
- B. \(21\)
Explanation
Positive diagonals: \(2\cdot3\cdot4+0\cdot2\cdot0+1\cdot1\cdot1=25\). Negative ones: \(1\cdot3\cdot0+2\cdot2\cdot1+0\cdot1\cdot4=4\). Result: \(25-4=21\).
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-003 Compute the determinant of the upper triangular matrix [1 2 3; 0 4 5; 0 0 6].
- 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-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)?