Exercise · ZW-DETERMINANT-001 · ★☆☆ Basic
Compute \(\det A\) for \(A=\begin{pmatrix}3 & 1 \\ 2 & 4\end{pmatrix}\).
Choose one option.
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- C. \(10\)
Explanation
For a \(2\times2\) matrix, \(\det A=ad-bc=3\cdot4-1\cdot2=10\). Adding the products (14) or reversing the order (\(-10\)) are sign errors.
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-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-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)?