Mathematics
Determinants
सारणिक
In this Class 12 Mathematics chapter, students learn determinants as a structured way to represent and analyze square matrices. They explore determinants of different orders, calculate them using minors and cofactors, and apply key properties to simplify evaluations. The chapter also develops methods for finding the area of a triangle using determinants and solving systems of linear equations through determinant-based techniques such as Cramer's rule, strengthening algebraic reasoning and accuracy.
1Determinant of a matrix
आव्यूह का सारणिक
In this Class 12 Mathematics topic, students learn how to define and evaluate the determinant of a square matrix, including determinants of orders two and three. They work with minors and cofactors, expand determinants along rows or columns, and apply key properties to simplify calculations. The topic also connects determinants with geometric ideas such as the area of a triangle and the condition for points to be collinear, strengthening algebraic reasoning and problem-solving within the chapter on Determinants.
0 questionsDeterminants of order 2 and 3
क्रम 2 और 3 के सारणिक
This Class 12 Mathematics topic in the chapter Determinants introduces students to determinants of order 2 and 3 and the methods used to evaluate them. Students learn the standard forms, expansion using minors and cofactors, signs in determinant expansion, and key properties that simplify calculations. The topic also builds a foundation for applying determinants to matrix-based problems and solving systems of linear equations.
0 questionsProperties of determinants
सारणिकों के गुणधर्म
In this Class 12 Mathematics topic from the chapter Determinants, students learn the fundamental properties that make determinants easier to evaluate and apply. They examine how interchanging rows or columns changes the sign, why equal or proportional rows and columns produce a zero determinant, and how common factors can be taken outside. The topic also develops understanding of linearity, transpose, and useful row and column transformations for simplifying calculations and solving determinant-based problems.
0 questionsMinors and cofactors
लघुक और सहगुणक
In this Class 12 Mathematics topic from the chapter Determinants, students learn how to find the minor of an element by deleting its corresponding row and column and evaluating the remaining determinant. They then use the sign factor (-1)^(i+j) to obtain the cofactor, understand the relationship between minors and cofactors, and apply these ideas to expand determinants along a row or column. The topic builds a foundation for solving determinant-based problems and finding the adjoint of a matrix.
0 questionsAdjoint of a matrix
आव्यूह का सहखंडज
In this Class 12 Mathematics topic from the chapter Determinants, students learn how to find the adjoint of a square matrix by calculating its cofactors and then transposing the cofactor matrix. The topic explains key properties such as A·adj(A) = |A|I and shows how the adjoint helps obtain the inverse of a matrix when its determinant is non-zero. Worked methods for small matrices strengthen calculation skills and support the solution of linear equations.
0 questionsInverse of a matrix
आव्यूह का प्रतिलोम
In this Class 12 Mathematics topic from the chapter Determinants, students learn what the inverse of a matrix is and when it exists. They study the condition that a square matrix must have a non-zero determinant, calculate the inverse using the adjoint method, and verify results through matrix multiplication. The topic also connects inverse matrices with solving systems of linear equations and develops accuracy in applying determinant and matrix properties.
0 questionsArea of triangle using determinants
सारणिकों द्वारा त्रिभुज का क्षेत्रफल
In this Class 12 Mathematics topic from the chapter Determinants, students learn how to find the area of a triangle when the coordinates of its three vertices are given. They use a 3×3 determinant, apply the area formula, and take the absolute value to obtain a positive result. The topic also helps students understand that a zero determinant indicates collinear points, so no triangle is formed, while reinforcing determinant expansion, coordinate substitution, and clear step-by-step algebraic calculation.
1 questionsSolving system of linear equations
रैखिक समीकरणों के निकाय का हल
In this Class 12 Mathematics topic, students learn to solve systems of linear equations using determinants. They work with coefficient and augmented matrices and apply methods such as Cramer’s rule to find unknowns. The topic also helps them identify whether a system has a unique solution, no solution, or infinitely many solutions by examining relevant determinant conditions. It strengthens algebraic reasoning and connects determinant calculations with systematic problem-solving.
0 questions