Class 12 Maths - ODISHA
Determinants
The chapter 'Determinants' in Class 12 Mathematics for Odisha BSE students builds upon matrices by assigning a unique scalar value to every square matrix. Students will learn how to evaluate determinants of order one, two, and three, along with properties of determinants that simplify complex calculations. Key topics include minors and cofactors, the adjoint of a matrix, and the inverse of a matrix. The chapter culminates in solving systems of linear equations using matrix inversion and Cramer's rule. This is a high-scoring unit frequently tested in board exams through both short-answer and long-answer questions.
Start Learning FreeKey Concepts
Determinant of a Square Matrix
A unique numerical value associated with every square matrix of order n, calculated by expanding along any row or column.
Minors and Cofactors
The minor of an element is the determinant obtained by deleting its row and column, while the cofactor includes a sign multiplier (-1)^(i+j).
Adjoint of a Matrix
The transpose of the cofactor matrix of a given square matrix A, denoted as adj(A).
Inverse of a Matrix
A matrix A^-1 exists if and only if A is a non-singular matrix (det(A) != 0), calculated as adj(A) divided by det(A).
Solution of Linear Equations
Using matrix equations of the form AX = B to find unknown variables, where X = A^-1 B.
Important Formulas
Board Exam Info
In the Odisha (BSE) Class 12 Mathematics board examination, Determinants typically carries around 8 to 12 marks. Questions frequently include evaluating 3x3 determinants using properties, finding the inverse of a matrix, and solving systems of three linear equations using matrix methods (long-answer type, usually 6 marks).
Frequently Asked Questions
What is the difference between a matrix and a determinant?
A matrix is an arrangement of numbers in rows and columns with no numerical value, whereas a determinant is a scalar value calculated from a square matrix.
Can rectangular matrices have determinants?
No, determinants can only be calculated for square matrices where the number of rows equals the number of columns.
When is a matrix called singular?
A square matrix is called singular if its determinant is equal to zero (det(A) = 0), meaning its inverse does not exist.
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