Exercise · ZW-DETERMINANT-004 · ★☆☆ Basic
For which value of \(k\) is \(\det\begin{pmatrix}k & 2 \\ 3 & 6\end{pmatrix}=0\)?
Choose one option.
Show answer
- B. \(k=1\)
Explanation
\(\det=6k-6=0\) gives \(k=1\): then the second row \((3,6)\) is three times the first \((1,2)\).
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-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)?