Maths Class 11 Chapter 3 Solution

• Our comprehensive Maths Class 11 Chapter 3 Solution will ensure you're fully prepared for your exams.
• Definition of Matrix with examples
• Definition of Row and Columns
• Definition of Entries or Elements 
• Definition of a rectangular Matrix with examples
• Definition of square Matrix with examples
• Definition of a diagonal Matrix with examples
• Definition of a square Matrix with examples
• Definition of unit Matrix or identity Matrix with examples
• Definition of null matrix or zero matrix with examples
• Definition of equal matrices with examples
• Definition of a transpose of a matrix with examples
• Solution of each question in Exercise 3.1
• Solution of each question in Exercise 3.2
• Solution of each question in Exercise 3.3
• Definition of a symmetric Matrix with examples
• Definition of skew-symmetric with exmaples
• Definitions of Hermitian Matrix and Skew-hermitians or Anti-hermitian with examples
• Definition of rank of a matrix 
• Solution of each question in Exercise 3.4
• Solution of each question in Exercise 3.5
• Note. If n is a positive integer, then A + A + A + .... to n times = nA.
• Note: The systems of linear equations involving the same variables, are equivalent if they have the same solution.
• Note: Matrices A and B are equivalent if B can be obtained by applying in turn a inite number of row operations on A.
• Two matrices are conformable for addition if they are of the same order. The sum A + B of two m % n matrices A = [aij] and B = [bij] is the m % n matrix C = [cij] formed by adding the corresponding entries of A and B together. In symbols, we write as C = A + B , that is: [cij] = [aij + bij] where cij = aij + bij for i = 1 , 2 , 3 , ...., m and j = 1, 2, 3, ..... , n. Note that aij + bij is the (i, j)th element of A + B.
• Multiplication of two Matrices: Two matrices A and B are said to be conformable for the product AB if the number of columns of A is equal to the number of rows of B. Let A = [aij] be a 2%3 matrix and B = [bij] be a 3x2 matrix. Then the product AB is deined to be the 2x2 matrix C whose element cij is the sum of products of the corresponding elements of the ith row of A with elements of jth column of B. The element c21 of C is shown in the igure (A), that is:
• Determinant of a 2 x 2 matrix: We can associate with every square matrix A over _ or C, a number |A|, known as the determinant of the matrix A. The determinant of a matrix is denoted by enclosing its square array between vertical bars instead of brackets. The number of elements in any row or column is called the order of determinant.
• Minor and Cofactor of an Element of a Matrix or its Determinant: Minor of an Element: Let us consider a square matrix A of order 3 .Then the minor of an element aij, denoted by .Mij is the determinant of the (3 - 1) x (3 - 1) matrix formed by deleting the ith row and the jth column of A(or|A|).
• Determinant of a Square Matrix of Order n83: The determinant of a square matrix of order n is the sum of the products of each element of row (or column) and its cofactor. The second scripts of positive terms are in circular order of anti-clockwise direction i.e., these are as 123, 231, 312 (adjoining igure) while the second scripts of negative terms are such as 132, 213, 321.