6. Systems, Sequences and Probability

Determinants — Quiz

Test your understanding of determinants with 5 practice questions.

Practice Questions

Question 1

What is the determinant of a scalar multiple of a $2 \times 2$ matrix? If $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ and $k$ is a scalar, what is $\det(kA)$?

Question 2

If a matrix $A$ has a determinant of $6$, and a new matrix $B$ is formed by swapping two rows of $A$, what is the determinant of $B$?

Question 3

Consider the matrix $A = \begin{pmatrix} 1 & 2 & 3 \\ 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix}$. What is its determinant?

Question 4

Which of the following statements correctly describes the relationship between the determinant of a matrix and the existence of a unique solution for a system of linear equations?

Question 5

What is the determinant of a $3 \times 3$ matrix where one column consists entirely of zeros?