Class 12 Maths - BIHAR
Matrices
The Matrices chapter in Class 12 Mathematics is fundamental for understanding linear algebra and serves as a powerful tool for solving systems of linear equations. For Bihar (BSEB) board students, this chapter is high-scoring and introduces the rectangular array of numbers, operations like matrix addition, scalar multiplication, and multiplication of matrices. You will also learn about transpose, symmetric and skew-symmetric matrices, and invertible matrices. Mastering these concepts is essential not just for this chapter, but also for scoring well in the subsequent chapter on Determinants, forming a combined weightage of around 10-15 marks in the final exam.
Start Learning FreeKey Concepts
Definition and Order of a Matrix
A matrix is an ordered rectangular array of numbers or functions. The order of a matrix is given by m x n, where m is the number of rows and n is the number of columns.
Types of Matrices
Matrices are classified into various types based on rows and columns, such as row matrix, column matrix, square matrix, diagonal matrix, scalar matrix, and identity matrix.
Matrix Operations
Matrices can be added or subtracted if they have the same order. Multiplication of two matrices A and B (AB) is possible only if the number of columns in A equals the number of rows in B.
Transpose of a Matrix
The transpose of a matrix is obtained by interchanging its rows and columns, denoted by A' or A^t. Properties include (A')' = A and (A + B)' = A' + B'.
Symmetric and Skew-Symmetric Matrices
A square matrix A is symmetric if A' = A and skew-symmetric if A' = -A. Every square matrix can be uniquely expressed as the sum of a symmetric and a skew-symmetric matrix.
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 I is the identity matrix.
Important Formulas
Board Exam Info
In the Bihar (BSEB) Class 12 Mathematics board exam, Matrices typically carries around 5 to 8 marks (combined with Determinants, the total weightage reaches 12-15 marks). Common question types include 1-mark objective (MCQs) on order and types of matrices, 2-mark short answer questions on matrix multiplication and transpose, and 5-mark long answer questions involving matrix equations or proving properties of symmetric and skew-symmetric matrices.
Frequently Asked Questions
Is matrix multiplication commutative?
No, matrix multiplication is generally not commutative, meaning AB is usually not equal to BA, even when both products are defined.
Can any two matrices be added?
No, two matrices can only be added or subtracted if they have the exact same order (same number of rows and columns).
What is the difference between a symmetric and a skew-symmetric matrix?
For a symmetric matrix, the transpose equals the original matrix (A' = A). For a skew-symmetric matrix, the transpose equals the negative of the original matrix (A' = -A), and all its diagonal elements must be zero.
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