Class 12 Maths - ODISHA
Matrices
The Matrices chapter in Class 12 Mathematics for Odisha BSE students introduces rectangular arrays of numbers, which are essential tools for solving system of linear equations efficiently. This chapter covers types of matrices, matrix operations like addition, multiplication, and the concept of transpose. You will also learn about invertible matrices and the inverse of a matrix using elementary transformations or adjoint methods. Matrices hold significant weight in the CHSE Odisha board exams, frequently appearing in both short answer and long answer sections. Mastering this chapter builds a strong foundation for determinants and linear programming.
Start Learning FreeKey Concepts
Definition and Order of a Matrix
A matrix is an ordered rectangular array of numbers or functions. If a matrix has 'm' rows and 'n' columns, its order is given as m × n.
Types of Matrices
Matrices are classified based on their dimensions and elements into row matrix, column matrix, square matrix, diagonal matrix, scalar matrix, and identity matrix.
Matrix Multiplication
Two matrices can be multiplied only if the number of columns in the first matrix equals the number of rows in the second matrix. Matrix multiplication is not commutative.
Transpose of a Matrix
The transpose of a matrix is obtained by interchanging its rows and columns. Symmetric matrices equal their transpose, while skew-symmetric matrices equal their negative transpose.
Inverse of a Matrix
A square matrix A is invertible if there exists a matrix B such that AB = BA = I. The inverse is calculated using the formula A inverse equals adjoint of A divided by the determinant of A.
Important Formulas
Board Exam Info
In the Odisha (BSE/CHSE) Class 12 Mathematics board examination, the Matrices chapter typically carries around 6 to 10 marks. Questions commonly include 1-mark objective questions, 2-mark short questions on finding matrix products or transposes, and 4 to 6-mark long questions involving solving linear equations using matrix inversion or proving properties of symmetric and skew-symmetric matrices.
Frequently Asked Questions
Is matrix multiplication commutative?
No, matrix multiplication is generally not commutative. That means AB does not equal BA in most cases.
What is the condition for finding the inverse of a matrix?
A matrix must be a square matrix and its determinant must not be equal to zero (non-singular matrix) to have an inverse.
How do we write the transpose of a matrix?
The transpose of matrix A is denoted by A' or A^T, and is formed by swapping its rows with columns.
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