Maths · Class 12 · Chapter 3
Matrices
13 lessons 111 min 2 simulations
A matrix is a rectangle of numbers read by row and column. This chapter names the shapes a matrix can take, says when two matrices are equal, and builds an algebra on them: addition and scaling entry by entry, multiplication row by column, the transpose, symmetric and skew symmetric matrices, and the inverse of a square matrix. Most of the ordinary rules of algebra survive, but two do not: a product can depend on the order of its factors, and two non-zero matrices can multiply to zero.
What the exam asks
JEE Main asks for the order of a product and whether it is defined, for a single entry of a product, and for powers such as A² or A³ fed into a polynomial like A² − 5A + 7I. It tests the transpose rules, above all (AB)′ = B′A′, and the facts that a skew symmetric matrix has a zero diagonal and that every square matrix splits into symmetric and skew symmetric parts. Marks are lost by assuming AB = BA, by expanding (A + B)² as A² + 2AB + B², and by cancelling a matrix from both sides of an equation.
Lessons
13 lessons · 111 min
1What a matrix isNCERT §3.1–3.27 min2Order and entriesNCERT §3.2.18 min3Types of matricesNCERT §3.37 min4Equal matricesNCERT §3.3.17 min5Adding and scalingNCERT §3.4.1–3.4.48 min6Multiplying row by columnNCERT §3.4.511 min 1 sim7Order matters in a productNCERT §3.4.512 min 1 sim8Laws of multiplicationNCERT §3.4.67 min9The transposeNCERT §3.57 min10Symmetric and skew symmetricNCERT §3.67 min11Invertible matricesNCERT §3.78 min12Powers and matrix equationsNCERT §3.4, Misc.8 min13Chapter reviewMust-know facts, traps and formulas14 min