Exercise · ZW-DETERMINANT-009 · ★★★ Advanced
Let \(A\) be a \(2\times2\) matrix with \(\det A=7\). What is \(\det(2A)\)?
Choose one option.
Show answer
- B. \(28\)
Explanation
Doubling every entry of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) gives \(2a\cdot2d-2b\cdot2c=4(ad-bc)=28\). The factor is \(2^2\), not \(2\).
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-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.