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Class 12 Maths Chapter 3 Ncert Solutions

NCERT Solutions for Class 12th Maths Chapter 3 Matrices

NCERT Solutions for class 12th maths chapter 3 Matrices are an invaluable resource for students seeking to excel in their mathematics studies. As one of the fundamental chapters in the curriculum, a thorough understanding of matrices is essential for advanced mathematical concepts. The NCERT Solutions provided for this chapter offer comprehensive explanations and step-by-step solutions to all the questions and exercises. These solutions are provided by subject experts in a well-structured manner, making it easier for students to learn and understand. Students can download PDF of the NCERT Solutions for class 12 maths to score better in exams.

All Exercise of Class 12th Maths Chapter 3 Matrices

On our website, Memorysclub provides NCERT Solutions for class 12 math, Along with additional resources such as sample papers, question banks, and study notes. We can also offer a section for students to ask their doubts and get them answered by experts.

Types of Matrices

Matrices, fundamental in various branches of mathematics and applications, come in different types, each with unique characteristics. Here’s an overview of some common types of matrices:

Row Matrix:
- Definition: A matrix with a single row and multiple columns.
- Example: $[�, �, �]$
Column Matrix:
- Definition: A matrix with a single column and multiple rows.
- Example: $[\begin{array}{c} � \\ � \\ � \end{array}]$
Square Matrix:
- Definition: A matrix with an equal number of rows and columns.
- Example: $[\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}]$
Zero or Null Matrix:
- Definition: A matrix where all elements are zero.
- Example: $[\begin{array}{cc} 0 & 0 \\ 0 & 0 \end{array}]$
Identity or Unit Matrix:
- Definition: A square matrix with diagonal elements equal to 1 and non-diagonal elements equal to 0.
- Example: $[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$
Diagonal Matrix:
- Definition: A square matrix where all non-diagonal elements are zero.
- Example: $[\begin{array}{ccc} 2 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 7 \end{array}]$
Scalar Matrix:
- Definition: A diagonal matrix where all diagonal elements are equal.
- Example: $[\begin{array}{ccc} � & 0 & 0 \\ 0 & � & 0 \\ 0 & 0 & � \end{array}]$
Symmetric Matrix:
- Definition: A matrix that is equal to its transpose.
- Example: $[\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{array}]$
Skew-Symmetric Matrix:
- Definition: A matrix where the transpose is equal to the negative of the original matrix.
- Example: $[\begin{array}{ccc} 0 & - 2 & 3 \\ 2 & 0 & - 5 \\ - 3 & 5 & 0 \end{array}]$

These types of matrices form the foundation for various mathematical operations, applications in physics, computer science, and engineering, making them indispensable tools in diverse fields. Understanding their properties is key to mastering linear algebra and its applications.

Important Formula for Class 12th Maths Chapter 3 Matrices

Matrices are essential mathematical tools used in various fields, and understanding key formulas is crucial for performing operations and solving problems. Here are some important formulas for matrices:

Addition and Subtraction:
- For matrices A and B of the same order (m x n): $(� \pm �)_{� �} = �_{� �} \pm �_{� �}$
Scalar Multiplication:
- For a matrix A and a scalar k: $(� �)_{� �} = � \cdot �_{� �}$

Matrix Multiplication:
- If A is an m x n matrix and B is an n x p matrix, the product C = AB is an m x p matrix.
- The element at the (i, j) position in C is given by: $(�)_{� �} = \sum_{� = 1}^{�} �_{� �} \cdot �_{� �}$
Identity Matrix:
- For an n x n identity matrix $�_{�}$
Transpose of a Matrix:
- If A is an m x n matrix, the transpose is an n x m matrix denoted by $�^{�}$
- The element at the (i, j) position in $�^{�}$
Determinant of a 2×2 Matrix:
- For a 2×2 matrix $� = [\begin{array}{cc} � & � \\ � & � \end{array}]$
Determinant of a 3×3 Matrix:
- For a 3×3 matrix $� = [\begin{array}{ccc} � & � & � \\ � & � & � \\ � & ℎ & � \end{array}]$
Inverse of a 2×2 Matrix:
- For a 2×2 matrix $� = [\begin{array}{cc} � & � \\ � & � \end{array}]$

These formulas form the basis for performing operations, solving systems of equations, and understanding the properties of matrices. Mastering these concepts is essential for success in linear algebra and its applications.