Class 12 CBSE Maths Syllabus
Chapter 1: Relations and Functions
Chapter 2: Inverse Trigonometric Functions
Chapter 3: Matrices
Chapter 4: Determinants
Chapter 5: Continuity and Differentiability
Chapter 6: Applications of Derivatives
Chapter 7: Integrals
Chapter 8: Applications of Integrals
Chapter 9: Differential Equations
Chapter 10: Vector Algebra
Chapter 11:3D Geometry
Chapter 12: Linear Programming
Chapter 13: Probability
Chapter 1: Relations and Functions
Chapter 2: Inverse Trigonometric Functions
Chapter 3: Matrices
Chapter 4: Determinants
Chapter 5: Continuity and Differentiability
Chapter 6: Applications of Derivatives
Chapter 7: Integrals
Chapter 8: Applications of Integrals
Chapter 9: Differential Equations
Chapter 10: Vector Algebra
Chapter 11:3D Geometry
Chapter 12: Linear Programming
Chapter 13: Probability
Introduction
Every chapter has some important points and highlights that give a gist of the topics covered in it. Students can refer to them while revising their concepts. They can find the important points to remember for this chapter below.
- A set of numbers (real or imaginary) or symbols or expressions arranged in the form of a rectangular array of m rows and n columns is called m×n matrix.
- A square matrix A=[aij]n×n is called an identity or a unit matrix, if aij=0 for all i≠j and aij=1 for all i=j.
- Commutativity: If A and B are two matrices of the same order, then A+B=B+A.
- Associativity: If A,B,C are three matrices of the same order, then (A+B)+C=A+(B+C).
- Existence of Identity: The null matrix is the identity element for matrix addition i.e., A+O=A=O+A
- Existence of Inverse: For every matrix A=[aij]m×n, there exists a matrix −A=[−aij]m×n, such that A+(−A)=O=(−A)+A
- Cancellation Laws: If A,B,C are three matrices of the same order, then A+B=A+C⇒B=C and, B+A=C+A⇒B=C
- In order to find the inverse of a non-singular square matrix A by elementary operations, we write A=IA or A=AI
- We perform a sequence of elementary row operations successively on A on the LHS and the pre-factor I on RHS till we obtain. The matrix B, so obtained, is the desired inverse of matrix A.
Exercises
Exercise 3.1
Exercise 3.2
Exercise 3.3
Exercise 3.4
Miscellaneous Exercise
*This YouTube playlist contains 62 videos of competitive examinations including objective and theory
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Very informative
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