Maths · Class 12 · Chapter 4
Determinants
11 lessons 93 min 2 simulations
A determinant is a single number computed from a square matrix. For a 2 × 2 matrix it is ad − bc, and it decides at once whether the matching pair of linear equations has exactly one solution. This chapter evaluates determinants of order 1, 2 and 3, uses them for the area of a triangle, builds minors, cofactors and the adjoint, finds A⁻¹ = (1/|A|) adj A, and solves systems AX = B by the matrix method, with a test for when a system has no solution.
What the exam asks
JEE Main asks for 3 × 3 determinants (expand along the row or column with most zeros), |kA| = kⁿ|A|, |adj A| = |A|ⁿ⁻¹, |AB| = |A||B| and |A⁻¹| = 1/|A|, areas and collinearity from ½|det|, the inverse by adjoint, and the consistency test for AX = B. Properties of determinants and Cramer's rule are outside the rationalised NCERT text but are standard JEE tools; they are collected in the last section. Marks go on sign slips in cofactors, on forgetting the power n in |kA|, and on calling a system with |A| = 0 inconsistent without checking (adj A)B.
Lessons
11 lessons · 93 min
1What a determinant isNCERT §4.1–4.2.17 min2Second-order determinantsNCERT §4.2.211 min 1 sim3Third-order determinantsNCERT §4.2.37 min4Area of a triangleNCERT §4.37 min5Minors and cofactorsNCERT §4.47 min6The adjointNCERT §4.5.17 min7Singular matrices and the inverseNCERT §4.57 min8Consistent and inconsistent systemsNCERT §4.611 min 1 sim9Solving by the matrix methodNCERT §4.6.18 min10Properties JEE addsNCERT §4.2, JEE extension7 min11Chapter reviewMust-know facts, traps and formulas14 min