Class 12 Maths - HARYANA
Matrices
The Matrices chapter in Class 12 Mathematics for the Haryana Board (BSEH) introduces rectangular arrays of numbers that simplify the handling of linear equations and data transformations. You will learn about different types of matrices like row, column, diagonal, and symmetric matrices, alongside essential operations including matrix addition, scalar multiplication, and matrix multiplication. A major focus is placed on finding the transpose of a matrix, elementary row and column operations, and calculating the inverse of a matrix using elementary transformations. Scoring well in this chapter is crucial as it forms the bedrock for determinants and linear programming in board exams.
Start Learning FreeKey Concepts
Definition and Order of a Matrix
A matrix is an ordered rectangular array of numbers. If a matrix has m rows and n columns, its order is written as m x n.
Types of Matrices
Matrices are classified into various types such as row, column, square, diagonal, scalar, identity, and zero matrices based on their shape and element distribution.
Matrix Multiplication
Two matrices A and B can be multiplied only if the number of columns in A equals the number of rows in B. Matrix multiplication is not commutative in general.
Transpose of a Matrix
The transpose of a matrix is obtained by interchanging its rows and columns, denoted by A'. It leads to symmetric and skew-symmetric matrices.
Invertible Matrices
A square matrix A of order n is invertible if there exists a square matrix B of the same order such that AB = BA = I, where B is the inverse of A.
Important Formulas
Board Exam Info
In the Haryana (BSEH) Class 12 Mathematics board examination, the Matrices chapter typically carries around 4 to 6 marks. Common question types include finding the product of two matrices, proving properties of transposes, expressing a square matrix as the sum of a symmetric and a skew-symmetric matrix, and finding the inverse of a 2x2 or 3x3 matrix using elementary row operations.
Frequently Asked Questions
Is matrix multiplication commutative?
No, matrix multiplication is generally not commutative, meaning AB is usually not equal to BA.
What is the difference between a symmetric and a skew-symmetric matrix?
For a symmetric matrix, the transpose equals the matrix itself (A' = A). For a skew-symmetric matrix, the transpose equals the negative of the matrix (A' = -A), and all its diagonal elements must be zero.
Can every matrix have an inverse?
No, only square matrices whose determinant is non-zero (non-singular matrices) possess an inverse.
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