Matrices
In Chapter 3 of NCERT textbook, we shall see the definition of a matrix, types of matrices, equality of matrices, operations on matrices such as the addition of matrices and multiplication of a matrix by a scalar, properties of matrix addition, properties of scalar multiplication, multiplication of matrices, properties of multiplication of matrices, transpose of a matrix, properties of the transpose of the matrix, symmetric and skew-symmetric matrices, elementary operation or transformation of a matrix, the inverse of a matrix by elementary operations and miscellaneous examples.
- Matrix: A matrix is said to have an ordered rectangular array of functions or numbers. A matrix of order m × n consists of m rows and n columns.
- Order of Matrix: If a matrix has m rows and n columns, then its order is written as m × n. If a matrix has order m × n, then it has mn elements
- Square Matrix: An m × n matrix will be known as a square matrix when m = n.
- Diagonal Matrix: A = [aij]m × m will be known as a diagonal matrix if aij = 0, when i ≠ j.
- Scalar Matrix: A = [aij]n × n is a scalar matrix if aij = 0, when i ≠ j, aij = k, (where k is some constant); and i = j.
- Identity Matrix: A = [aij]n × n is an identity matrix, if aij = 1, when i = j and aij = 0, when i ≠ j.
- Zero Matrix: A zero matrix will contain all its elements as zero.
- Column Matrix: A matrix which is of the form [A]n×1 is called the column matrix.
- Row Matrix: A matrix that is of the form [A]1×n is called the row matrix.
- A = [aij] = [bij] = B if and only if:
- A and B are of the same order
- aij = bij for all the certain values of i and j
- Operations on Matrices: Between two or more two matrices, the following operations are defined below:
- Addition of Matrix: If A = [aij]m×n and B = [yij]m×n, then A + B = [aij +bij]m×n, 1 ≤ i ≤ m, 1 ≤ j ≤ n
- Subtraction of Matrix: If A = [aij]m×n and B = [bij]m×n, then A – B = [aij – bij]m×n, 1 ≤ i ≤ m, 1 ≤ j ≤ n
- Multiplication of a matrix by scalar number: Let A = [aij]m×n be a matrix and k is scalar, then kA is another matrix obtained by multiplying each element of A by the scalar k, i.e. if A = [aij]m×n, then kA = [kaij]m×n
- Multiplication of Matrices: Let A and B be two matrices. Then, their product AB is defined, if the number of columns in matrix A is equal to the number of rows in matrix B.
Class 12 Maths Formulas
Class 12 maths formulas page is designed for the convenience of the learners so that one can understand all the important concepts of Class 12 Mathematics directly and easily. Math formulae for Class 12 are for the students who find mathematics to be a nightmare and difficult to grasp. They may become hesitant and lose interest in studies as a result of this. We have included all of the key formulae for the 12th standard Maths topic, which students may simply recall, to assist them in understanding Maths in a straightforward manner. For all courses such as Integration, Differentiation, Trignometry, Relation and Functions, and so on, the formulae are provided here according to the NCERT curriculum.
Table of Content
- Chapter 1: Relations and Functions
- Chapter 2: Inverse Trigonometric Functions
- Chapter 3: Matrices
- Chapter 4: Determinants
- Chapter 5: Continuity and Differentiability
- Chapter 6: Applications of Derivatives
- Chapter 7: Integrals
- Chapter 8: Applications of Integrals
- Chapter 9: Differential Equations
- Chapter 10: Vector Algebra
- Chapter 11: Three-Dimensional Geometry
- Chapter 12: Linear Programming
- Chapter 13: Probability