NCERT Solutions for Class 12 Mathematics Chapter 4 Determinants
NCERT Solutions for Class 12 Mathematics Chapter 4 Determinants covers the determinant of a square matrix and its properties, finding the area of a triangle using determinants, the adjoint and inverse of a matrix, and solving systems of linear equations.
Overview of Topics & Subtopics (Click to Jump)
1. Determinant and Its Properties
Short Note:
• The determinant of a square matrix is a scalar value computed from its elements; for a 2×2 matrix [[a, b], [c, d]], it equals ad - bc.
• Key properties include: the determinant changes sign when two rows/columns are interchanged, and it equals zero if any two rows/columns are identical or proportional.
2. Application: Area of a Triangle
Short Note:
• The area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3) can be expressed as half the absolute value of a 3×3 determinant formed from the coordinates.
• If the computed determinant is zero, the three points are collinear and do not form a triangle.
3. Adjoint, Inverse and Cramer's Rule
Short Note:
• The adjoint of a matrix A is the transpose of its cofactor matrix, and satisfies A · (adj A) = |A| · I, leading to the inverse formula A⁻¹ = (1/|A|) adj A.
• Cramer's rule uses determinants to directly solve a system of linear equations when the coefficient determinant is non-zero, yielding a unique solution.
NCERT Textbook Exercise Questions
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These short notes are designed for quick revision. Read the main points once, then use the related material below to practise the same chapter. Revising a concept and checking it with questions can make your preparation more focused.