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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, a matrix is skew‑symmetric when . Hence is skew‑symmetric. Question 2: Show that is symmetric or skew‑symmetric according as is symmetric or skew‑symmetric. Solution: Step 1 Recall […]

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 , are inverses of each other if and only if each is the multiplicative inverse of the other, i.e., This relation guarantees that both left‑ 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 If and verify that(i) (ii) Solution 2 (i) Compute : Then Now compute : Thus (i) is verified. (ii) Compute : Then Thus (ii) is

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)  Solutions: (i) (ii) Add entry‑wise: (iii) (iv) Use : Question 3. Compute (i) Solution Entry (1,1):  Entry (1,2):  Entry (2,1):  Entry (2,2):  (ii) The first matrix is 3 × 1 (column) and the second

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 are the possible orders it can have? What, if it has 13 elements? Solution: If a matrix has 24 elements, we list all possible ordered pairs

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 , where Solution:Let , where . Then, Now, we know Therefore, Substituting the value of , Question 3: Simplify: , where Solution:Let , then and So

Derivative of Trigonometric Functions Derivative of Inverse Trigonometric Functions

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 and the codomain. A function associates each element in the domain with a unique element in the codomain, and it is often represented as a