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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: $[\ufffd,\ufffd,\ufffd]$[a,b,c]

Column Matrix:

- Definition: A matrix with a single column and multiple rows.
- Example: $\left[\begin{array}{c}{\textstyle \ufffd}\\ {\textstyle \ufffd}\\ {\textstyle \ufffd}\end{array}\right]$⎣⎡xyz⎦⎤

Square Matrix:

- Definition: A matrix with an equal number of rows and columns.
- Example: $\left[\begin{array}{ccc}{\textstyle 1}& {\textstyle 2}& {\textstyle 3}\\ {\textstyle 4}& {\textstyle 5}& {\textstyle 6}\\ {\textstyle 7}& {\textstyle 8}& {\textstyle 9}\end{array}\right]$⎣⎡147258369⎦⎤

Zero or Null Matrix:

- Definition: A matrix where all elements are zero.
- Example: $\left[\begin{array}{cc}{\textstyle 0}& {\textstyle 0}\\ {\textstyle 0}& {\textstyle 0}\end{array}\right]$[0000]

Identity or Unit Matrix:

- Definition: A square matrix with diagonal elements equal to 1 and non-diagonal elements equal to 0.
- Example: $\left[\begin{array}{ccc}{\textstyle 1}& {\textstyle 0}& {\textstyle 0}\\ {\textstyle 0}& {\textstyle 1}& {\textstyle 0}\\ {\textstyle 0}& {\textstyle 0}& {\textstyle 1}\end{array}\right]$⎣⎡100010001⎦⎤

Diagonal Matrix:

- Definition: A square matrix where all non-diagonal elements are zero.
- Example: $\left[\begin{array}{ccc}{\textstyle 2}& {\textstyle 0}& {\textstyle 0}\\ {\textstyle 0}& {\textstyle 5}& {\textstyle 0}\\ {\textstyle 0}& {\textstyle 0}& {\textstyle 7}\end{array}\right]$⎣⎡200050007⎦⎤

Scalar Matrix:

- Definition: A diagonal matrix where all diagonal elements are equal.
- Example: $\left[\begin{array}{ccc}{\textstyle \ufffd}& {\textstyle 0}& {\textstyle 0}\\ {\textstyle 0}& {\textstyle \ufffd}& {\textstyle 0}\\ {\textstyle 0}& {\textstyle 0}& {\textstyle \ufffd}\end{array}\right]$⎣⎡k000k000k⎦⎤

Symmetric Matrix:

- Definition: A matrix that is equal to its transpose.
- Example: $\left[\begin{array}{ccc}{\textstyle 1}& {\textstyle 2}& {\textstyle 3}\\ {\textstyle 2}& {\textstyle 4}& {\textstyle 5}\\ {\textstyle 3}& {\textstyle 5}& {\textstyle 6}\end{array}\right]$⎣⎡12