Class 12 Mathematics — Chapter 4: Determinants

What you'll learn

• ▸Determinant of a Square Matrix
• ▸Calculating Determinant of a 2x2 Matrix
• ▸Expansion of a 3x3 Determinant
• ▸Sign Convention for Expansion
• ▸Property of Scalar Multiplication of a Matrix
• ▸Solving Equations with Determinants
• ▸Area of a Triangle using Determinants
• ▸Condition for Collinearity

Chapter Summary

--- PAGE 1 --- Chapter 4 DETERMINANTS ✧ All Mathematical truths are relative and conditional. — C.P. STEINMETZ ✧ 4.1 Introduction In the previous chapter, we have studied about matrices and algebra of matrices. We have also learnt that a system of algebraic equations can be expressed in the form of matrices. This means, a system of linear equations like a₁x + b₁y = c₁ a₂x + b₂y = c₂ can be represented as [ a₁ b₁ ] [ x ] = [ c₁ ]. Now, this [ a₂ b₂ ] [ y ] [ c₂ ] system of equations has a unique solution or not, is determined by the number a₁b₂ - a₂b₁. (Recall that if a₁ b₁ — ≠ — or, a₁b₂ - a₂b₁ ≠ 0, then the system of linear P.S. Laplace a₂ b₂ (1749-1827) equations has a unique solution). The number a₁b₂ - a₂b₁ which determines uniqueness of solution is associated with the matrix A = [ a₁ b₁ ] …

Practice Questions from this Chapter

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1. Explain how matrices help computers. Get Solution →
2. Show a real-world use for determinants. Get Solution →
3. Calculate a 3x3 determinant quickly. Get Solution →
4. According to the text, what types of matrices have determinants? Get Solution →
5. What is the determinant of a matrix of order one, A = [a]? Get Solution →
6. What is the correct formula to calculate the determinant of a 2x2 matrix A = [ a b ; c d ]? Get Solution →
7. How should the notation |A| be read when A is a matrix? Get Solution →
8. The minor of an element aᵢⱼ is a determinant of what order, if the original matrix is of order n (where n ≥ 2)? Get Solution →

Did you know?

• 💡 The word "matrix" comes from the Latin word for "womb" or "breeding place".
• 💡 The largest known prime number has over 24 million digits and would fill a book.
• 💡 Computer graphics and video games use matrices to rotate and scale 3D objects.
• 💡 Early forms of determinants were used in ancient China to solve systems of equations.
• 💡 There are more possible chess game positions than atoms in the observable universe.

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