Exercise · ZW-DETERMINANT-007 · ★★☆ Intermediate
The parallelogram spanned by the vectors \((3,1)\) and \((1,2)\) has area:
Choose one option.
Show answer
- A. \(5\)
Explanation
The area is \(|\det|\) of the matrix with those vectors as rows: \(|3\cdot2-1\cdot1|=5\).
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-006 Compute det A using the rule of Sarrus for A=[2 0 1; 1 3 2; 0 1 4].
- 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)?