Maths Class 11 Chapter 3 Notes

• Our comprehensive Maths Class 11 Chapter 3 Notes will ensure you're fully prepared for your exams.
• Definition of unit Matrix with examples
• Definition of column Matrix with example
• Definition of a symmetric matrix with examples
• Definition of skew-symmetric matrix with examples
• Definition of a diagonal Matrix with examples
• Transpose of a matrix with example
• Cofactor of an element with an example
• Square Matrix with example
• Definition of Principal diagonal matrix with examples
• Definition of a secondary diagonal  matrix with examples
• Definition of Row Matrix with examples
• Definition of Column Matrix with examples
• Definition of Scalar Matrix with examples
• Definition of Multiplication of two matrices with examples
• What is the row operation and column operation, upper triangular Matrix with examples a lower triangular Matrix with examples hermitian Matrix with examples of triangular Matrix with examples the skew hermitian Matrix with examples, symmetric matrix with examples of the skew-symmetric matrix with examples.
• Reduced Echelon form of matrix with examples
• What is the consistency of a system and inconsistency of a system with examples?
• The method how to solve non Homogeneous Linear Equations with examples
• Cramer's Rules with examples.
• Rectangular Matrix: If m ≠ n, then the matrix is called a rectangular matrix of order m %n, that is, the matrix in which the number of rows is not equal to the number of columns, is said to be a rectangular matrix.
• Square Matrix: If m = n, then the matrix of order m % n is said to be a square matrix of order n or m. i.e., the matrix which has the same number of rows and columns is called a square matrix.
• Diagonal Matrix: Let A = [aij] be a square matrix of order n. If aij = 0 for all i ≠ j and at least one aij ≠ 0 for i = j, that is, some elements of the principal diagonal of A may be zero but not all, then the matrix A is called a diagonal matrix.
• Scalar Matrix: Let A = [aij] be a square matrix of order n. If aij = 0 for all i ≠ j and aij = k (some non-zero scalar) for all i = j, then the matrix A is called a scalar matrix of order n. 
• Unit Matrix or Identity Matrix : Let A = [aij] be a square matrix of order n. If aij = 0 for all i ≠ j and aij = 1 for all i = j, then the matrix A is called a unit matrix or identity matrix of order n. We denote such matrix by In and it is of the form:
• Null Matrix or Zero Matrix : A square or rectangular matrix whose each element is zero, is called a null or zero matrix. An m % n matrix with all its elements equal to zero, is denoted by Om%n. Null matrices may be of any order.
• Transpose of a Matrix: If A is a matrix of order m % n then an n % m matrix obtained by interchanging the rows and columns of A, is called the transpose of A. It is denoted by A t. If [aij]m%n then the transpose of A is deined as: At = [a’ij] n%m where a’ij= aji .. for i = 1, 2, 3, ...., n and j = 1, 2, 3, ..... , m.
• Equal Matrices: Two matrices of the same order are said to be equal if their corresponding entries are equal. For example, A = [aij]m%n and B = [bij]m%n are equal, i.e., A = B iff aij = bij for i = 1 , 2 , 3 , ...., m, j = 1, 2, 3, ..... , n. In other words, A and B represent the same matrix.

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