Ex-3.2 Q 1,2 | Chapter 3 | Matrices | Class 12th NCERT Math |

Introduction

This tutorial provides a step-by-step guide to solving questions 1 and 2 from Exercise 3.2 of the Class 12 NCERT Mathematics textbook, focusing on matrices. The methods demonstrated in this guide will help you understand matrix operations and their applications, ensuring a solid grasp of the topic.

Step 1: Understand the Basics of Matrices

Before diving into the exercise, ensure you are familiar with the following concepts:

• Matrix Definition: A matrix is a rectangular array of numbers arranged in rows and columns.
• Types of Matrices:
  • Row Matrix: A matrix with a single row.
  • Column Matrix: A matrix with a single column.
  • Square Matrix: A matrix with the same number of rows and columns.
• Matrix Operations: Addition, subtraction, and multiplication of matrices.

Step 2: Review the Exercise Questions

For Exercise 3.2, we will focus on:

• Question 1: This question typically involves performing operations such as addition or subtraction of given matrices.
• Question 2: This question may require you to apply matrix multiplication or find the transpose.

Question 1 Breakdown

1. Identify the given matrices and their dimensions.
2. Perform the required operation (addition/subtraction):
   • Ensure both matrices have the same dimensions.
   • Add or subtract corresponding elements.

Question 2 Breakdown

1. Identify the matrices involved in the multiplication.
2. Check if the multiplication is feasible (the number of columns in the first matrix must equal the number of rows in the second matrix).
3. Multiply the matrices:
   • Use the formula for matrix multiplication, where each element in the resulting matrix is the sum of the products of the corresponding row and column elements.

Step 3: Solve Question 1

1. Write down the matrices.
2. Perform the operation step by step:
   • Example for addition:
     • If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then:

       A + B = [[1+5, 2+6], [3+7, 4+8]]
              = [[6, 8], [10, 12]]
       

Step 4: Solve Question 2

1. Write down the matrices for multiplication.
2. Perform matrix multiplication:
   • Example:
     • If A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], then:

       A * B = [[1*5 + 2*7, 1*6 + 2*8],
                 [3*5 + 4*7, 3*6 + 4*8]]
             = [[19, 22],
                [43, 50]]
       

Conclusion

In this tutorial, we covered the fundamental concepts of matrices, along with detailed steps to solve Exercise 3.2 Questions 1 and 2 from the Class 12 NCERT Mathematics textbook. Practice these steps to reinforce your understanding of matrix operations. For further practice, explore additional exercises in the textbook or watch related videos for more examples.