Скачать или смотреть Class 12 Maths | Chapter 3 | Matrices | Exercise 3.2 | Question 18

In this video, you will get a solution for Question 18 of exercise 3.2 of Chapter 3 Matrices.

Welcome to Exercise 3.2 of Chapter 3: Matrices from the Class 12 Mathematics curriculum. This exercise focuses on the foundational concepts of matrices, ensuring that you have a solid understanding of their basic properties and operations.

Whether you're a student striving for top grades or an educator seeking effective teaching resources, this video is your ultimate companion in unraveling the mysteries of matrices. Join us on this educational journey as we empower you with the knowledge and skills to excel in Class 12 Mathematics.

Notes for Exercise 3.2


Time Stamps
0:00 Intro
0:08 Question 18
0:30 Solution
4:56 Outro

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Short Notes On Matrices

Definition: A matrix is a rectangular array of numbers arranged in rows and columns.
Notation: Matrices are typically denoted by capital letters (e.g., A, B, C), and elements within a matrix are denoted by lowercase letters with subscripts (e.g., a_ij represents the element in the ith row and jth column of matrix A).
Types of Matrices

Row Matrix: A matrix with a single row (e.g., A = [a1 a2 a3]).
Column Matrix: A matrix with a single column (e.g., B = [b1; b2; b3]).
Square Matrix: A matrix with an equal number of rows and columns (e.g., 2x2, 3x3 matrices).
Rectangular Matrix: A matrix with an unequal number of rows and columns.
Zero Matrix: A matrix in which all elements are zero (e.g., O = [0 0; 0 0]).
Identity Matrix: A square matrix with ones on the diagonal and zeros elsewhere (e.g., I = [1 0; 0 1]).
Order of a Matrix

The order of a matrix is defined by the number of rows (m) and columns (n), represented as m × n. For example, a 3 × 2 matrix has 3 rows and 2 columns.
Equality of Matrices

Two matrices are said to be equal if they have the same order and their corresponding elements are equal. For matrices A and B, A = B if and only if a_ij = b_ij for all i and j.
Addition and Subtraction of Matrices

Addition: Matrices of the same order can be added by adding their corresponding elements. If A = [a_ij] and B = [b_ij], then A + B = [a_ij + b_ij].
Subtraction: Similarly, matrices of the same order can be subtracted by subtracting their corresponding elements. If A = [a_ij] and B = [b_ij], then A - B = [a_ij - b_ij].
Important Keywords and Concepts
Matrix: An arrangement of numbers in rows and columns.
Element: An individual item or number in a matrix.
Row: A horizontal line of elements in a matrix.
Column: A vertical line of elements in a matrix.
Order of a Matrix: The dimensions of a matrix, given by the number of rows and columns (m × n).
Row Matrix: A matrix with a single row.
Column Matrix: A matrix with a single column.
Square Matrix: A matrix with an equal number of rows and columns.
Rectangular Matrix: A matrix with different numbers of rows and columns.
Zero Matrix: A matrix with all elements being zero.
Identity Matrix: A square matrix with 1's on the diagonal and 0's elsewhere.
Equal Matrices: Matrices that have the same order and identical corresponding elements.
Matrix Addition: The process of adding two matrices by adding their corresponding elements.
Matrix Subtraction: The process of subtracting one matrix from another by subtracting their corresponding elements.

Practice Problems
This chapter (Matrices) includes a variety of problems designed to test your understanding of the above concepts. You will be asked to:

Identify the order of given matrices.
Determine if two matrices are equal.
Perform addition and subtraction of matrices.
Classify matrices based on their types.
By working through these problems, you will strengthen your foundational knowledge of matrices and prepare yourself for more advanced topics in the subsequent exercises.

This detailed overview of Matrices provides you with a clear understanding of what to expect and the important keywords you need to know. Dive into the exercise, practice diligently, and master the basics of matrices to build a strong mathematical foundation.

This description provides a comprehensive overview of Matrices, covering key topics, important keywords, and a summary of practice problems. It ensures that students are well-prepared to tackle the exercise and understand the fundamental concepts of matrices.