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Matrices and Determinants, Class 12, Mathematics (IIT) Chapter Notes PDF Download

Definition of Matrix and Types of Matrices - Matrices and Determinants, Class 12, Mathematics


A. DEFINITION
Any rectangular arrangement of numbers (real or complex) (or of real valued or complex valued expressions) is called a matrix. If a matrix has m rows and n columns then the order of matrix is said to be m by n (denoted as m × n).
The general m × n matrix is A = CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants


where aij denote the element of ith row & jth column. The above matrix is usually denoted as [aij]m × n


Note :
(i) The elements a11, a22, a33,....... are called as diagonal elements. Their sum is called as trace of A denoted as tr(A)
(ii) Capital letters of English alphabets are used to denote matrices.


B. TYPES OF MATRICES


(i) Row Matrix : A matrix having only one row is called as row matrix (or row vector).
General form of row matrix is A = CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants


(ii) Column Matrix : A matrix having only one column is called as column matrix
(or column vector). General form of A = CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants


(iii) Square Matrix : A matrix in which number of rows & columns are equal is called a square
matrix. The general form of a square matrix is A = CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants


(iv) Zero Matrix : A = CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants


(v) Upper Triangular Matrix :

A = CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants
(i.e., all the elements below the diagonal element are zero.)


(vi) Lower Triangular Matrix :

A = CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants
(i.e., all the elements above the diagonal elements are zero.)


(vii) Diagonal matrix : CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants
(i.e., all the elements of the square matrix other than diagonal elements are zero)
Note : Diagonal matrix of order in is denoted as Diag (a11, a22,....... ann).


(viii) Scalar Matrix : Scalar matrix is a diagonal matrix in which all the diagonal elements are same.
CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants


(ix) Unit Matrix (Identity Matrix) : Unit matrix is a diagonal matrix in which all the diagonal elements
are unity. Unit matrix of order ‘n’ is denoted y In (or I).
CBSE, Class 11, IIT JEE, Syllabus, Preparation, NCERT, Important, matrices, determinants

 

 

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FAQs on Matrices and Determinants, Class 12, Mathematics (IIT) Chapter Notes

1. What are matrices?
Ans. Matrices are rectangular arrays of numbers or symbols arranged in rows and columns. Matrices play a significant role in many branches of mathematics, particularly in linear algebra.
2. What are determinants?
Ans. Determinants are scalar values that can be computed from square matrices. They are used to study properties of matrices and to solve systems of linear equations. Determinants can be used to determine if a matrix is invertible, which is a useful property for solving systems of equations.
3. How are matrices and determinants related?
Ans. Determinants are used to study matrices. For example, the determinant of a matrix can be used to determine if the matrix is invertible, which is a useful property for solving systems of equations. Determinants can also be used to find the eigenvalues and eigenvectors of a matrix.
4. What are some applications of matrices and determinants in real life?
Ans. Matrices and determinants are used in a variety of fields, including engineering, physics, computer science, and economics. For example, matrices can be used to model traffic flow, analyze social networks, and simulate chemical reactions. Determinants can be used to solve systems of linear equations, which is a common problem in many fields.
5. How can I prepare for the matrix and determinant section of the Class 12 Mathematics (IIT) exam?
Ans. To prepare for the matrix and determinant section of the Class 12 Mathematics (IIT) exam, students should familiarize themselves with the basic concepts and formulas related to matrices and determinants. They should also practice solving problems and exercises from textbooks and sample papers. Additionally, students can use online resources such as videos, tutorials, and practice tests to supplement their learning.
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