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

If 2a + b = 10 and a - b = 4, what is the value of a?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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If two complementary angles differ by 30°, what are the angles?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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What is the area of a circle with a diameter of 14 cm?

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

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A sphere has a radius of 7 cm. What is its volume?

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If 8x = 512, what is the value of x?

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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