Question 1: If and are symmetric matrices, prove that is a skew‑symmetric matrix. Solution: Because and are symmetric, their transposes equal themselves: and . Consider the transpose of : By definition,

Question 1: Matrices A and B will be inverse of each other only if (A) (B) (C) , (D) Solution: Two square matrices of the same order, say and ,

Question 1: Find the transpose of each of the following matrices: (i) (ii) (iii) Solution 1: (i) Let . Then (ii) Let . Then (iii) Let . Then Question 2

Question 1:  Let Find: (i)  (ii)  (iii)  (iv)  (v)  Solution(i)   (ii)  (iii)  (iv)   Row 1 × Col 1 :  Row 1 × Col 2 :  Row 2 × Col 1 :  Row 2 × Col 2 :  (v)  Row 1 × Col 1 :  Row 1 × Col 2 :  Row 2 × Col 1 :  Row 2 × Col 2 :  Question 2: Compute the following (i)  (ii)  (iii)  (iv) 

Question 1. In the matrix Solution: (i) The order of the matrix is  (ii) The number of elements is  (iii) Elements:  Question 2. If a matrix has 24 elements, what

Chapter 2: Inverse Trigonometric Functions Board: CBSE Question 1: Prove that Solution:Let , where . Then, Now, we know Therefore, Substituting the value of , Question 2: Prove that ,

Derivative of Trigonometric Functions Derivative of Inverse Trigonometric Functions

Formulas in NCERT 1. 2. 3. Other Important formulas to calculate limits 4. 5. 6. 7. 8. 9. 10.

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. The distance from the center to

Class 10 Board Preparation for Maths

Introduction and Definition of a Function In mathematics, a function is a fundamental concept that describes a specific type of relation between elements of two sets, typically called the domain

Cartesian Product The Cartesian product of two sets A and B, denoted as A × B, is a set that contains all possible ordered pairs where the first element of

Integration formulas for exponential functions For n≠−1 For a≠1 Integration formulas for Trigonometric Functions Integral formulas for some special functions.

Pythagorean Identities Reciprocal Identities Quotient Identities Co-function Identities (Complimentary angles)