Topic Details (Notes format)

How to Calculate Determinants of 2x2 and 3x3 Matrices

Subject: Mathematics

Book: Maths Mastery

A determinant signals properties like invertibility, with 2×2 determinant = ad – bc for matrix [[a, b], [c, d]]. For a 3×3 matrix, the Sarrus rule or expansion by minors is used. Example: For [[1, 2, 3], [4, 5, 6], [7, 8, 9]], applying Sarrus reveals a 0 determinant, meaning the matrix is not invertible. Determinants appear in geometry (volumes, areas), system solvability checks, and transformations. Understanding how to compute them quickly is key for advanced linear algebra, physics, and engineering tasks that rely on matrix operations.

Practice Questions

The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

View Question

A train 150 m long passes a pole in 15 seconds. What is its speed?

View Question

A car covers a distance of 150 km in 2.5 hours. What is its average speed?

View Question

The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

View Question

The area of an equilateral triangle with side length 6 cm is:

View Question

What is the LCM of 15 and 20?

View Question

If the length of a rectangle is doubled and the width is halved, what is the change in area?

View Question

What is the area of an equilateral triangle with side length 10 cm?

View Question

If a:b = 2:3 and b:c = 4:5, what is a:c?

View Question

A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

View Question