Determinant of 2×2
ad − bc; zero means not invertible.
Key idea
ad − bc; zero means not invertible.
In depth
For [a b; c d], det = ad − bc. It gives the signed area scaling of the transformation. Zero determinant means the matrix squashes the plane onto a line and has no inverse.
Worked example
det [3 1; 2 4] = 12 − 2 = 10.
Formula
Real-world uses
- Testing if a pair of linear equations has a unique solution
- Computing area of a parallelogram
Common mistake
Computing ac − bd.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Determinant of 2×2?
ad − bc; zero means not invertible. It is a topic at the advanced level in Linear Algebra.
What is the formula for Determinant of 2×2?
The key formula is det = ad − bc.
Where is Determinant of 2×2 used in real life?
Real-world examples: Testing if a pair of linear equations has a unique solution; Computing area of a parallelogram.
What should I learn before Determinant of 2×2?
Make sure you are comfortable with Inverse by Row Reduction, the previous topic in Linear Algebra.
What is a common mistake with Determinant of 2×2?
Computing ac − bd.
How can I practise Determinant of 2×2?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Determinant of 2×2?
Move on to Determinant of 3×3 next.
Related advanced topics in Linear Algebra
- Dot Product – Sum of component products.
- Angle Between Vectors – Cosine from the dot product.
- Orthogonality – Vectors are orthogonal when their dot product is 0.
- Projection – Component of one vector along another.
- Cross Product – A vector perpendicular to two vectors in 3D.
- Lines and Planes in Vector Form – Parametric and normal equations.