5. Inverses and Determinants

Connecting Determinant To Geometry — Quiz

Test your understanding of connecting determinant to geometry with 5 practice questions.

Practice Questions

Question 1

For a $2\times 2$ matrix $A$, the determinant is $\det(A)=5$. What is the area of the image of the unit square under the transformation defined by $A$?

Question 2

A linear transformation has determinant $-3$. What does the negative sign tell you about the transformation?

Question 3

What does a determinant of $0$ mean geometrically for a linear transformation?

Question 4

A $2\times 2$ matrix sends the unit square to a parallelogram with determinant $8$. What is the area of that parallelogram?

Question 5

The vectors $\mathbf{u}=(1,2)$ and $\mathbf{v}=(3,1)$ form a parallelogram. What is its area?