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Determinants form a very important part of the Class 12 Mathematics curriculum, and mastery of this topic helps in understanding many concepts in linear algebra, matrices, and even advanced mathematics. We will discuss here some of the important questions and concepts related to determinants with an emphasis on topics most likely to appear in Class 12 exams. Familiarity with these questions will not only help the students score better but will also enhance their overall understanding of the subject.
Maths Chapter 4 is very important for the students as many questions are framed from this chapter in board examinations. In CBSE Class 12 Maths Chapter 4 Important Questions, you understand the various important concepts like Determinant Definition, properties, area of a Triangle, minors and cofactors, adjoint and the inverse of a matrix, determinants, and matrix applications.
PREMIUM EDUCART QUESTIONS
(Most Important Questions of this Chapter from our📕)
In the table below, we have provided the links to Determinants Class 12 Maths Most Important Questions PDFs. You can download them without having to share any login info.
Before discussing important questions on determinants, it is important to know the definition. A determinant is a scalar quantity derived from the elements of a square matrix, which carry some features regarding that matrix. It is represented by det(A) or |A|, in which A refers to the given matrix in a question. The determinant is an important term that tells about the invertibility of the matrix and gives some information about the geometric properties of the transformations.
Important properties of determinants, which every student must know, are as follows:
In this section, we will cover the key topics and the important questions on the Class 12 determinants.
The problem that students generally face while solving the determinants chapter is finding a matrix determinant, especially for 3×3 and larger matrices. To be successful in this area, students need to master the cofactor expansion method and row or column operations.
A large proportion of the exam questions test the student's understanding of properties of determinants, particularly in terms of showing whether a matrix is singular or nonsingular and in using determinants to solve systems of linear equations.
Another important application for which determinants are essential is in finding the inverse of a matrix. A matrix is invertible if and only if its determinant is non-zero.
Important Questions
Here are some of the Important questions on Determinants.
1. Given the matrix: A = [ 2 1 3 ]
[ 4 1 2 ]
[ 6 1 4 ]
Find det(A) using cofactor expansion along the first row.
2. Given the matrix: A = [ 1 2 3 4 ]
[ 0 1 2 3 ]
[ 1 0 1 2 ]
[ 2 1 0 1 ]
Find det(A) using cofactor expansion along the first row.
3. If A = [ 2 1 3 ]
[ 4 1 3 ]
[ 6 1 3 ]
Prove that det(A) = 0.
4. Consider the matrix: A = [ 2 1 1 ]
[ 3 2 1 ]
[ 1 1 1 ]
Perform a row operation like R2 -> R2 - 3R1 and calculate the new determinant.
5. A = [ 1 2 ]
[ 3 4 ]
Find A⁻¹ using the determinant method.
6. Given the vertices A(1, 2), B(4, 6), and C(7, 8), use determinants to find the area of the triangle.
7. Given the matrix: A =[ 1 2 3 ]
[ 0 1 4 ]
[ 5 6 0 ]
Find A{-1} using determinants.
8. Given the matrix: A = [ 3 1 2 ]
[ 1 1 1 ]
[ 4 2 1 ]
Perform row operations to simplify the matrix and calculate the determinant.
9. A = [ 1 0 0 ]
[ 0 0 0 ]
[ 0 0 1 ]
Find det(A).
10. Find the rank of the matrix by evaluating its minors and determinants.
A = [ 1 2 3 ]
[ 2 4 6 ]
[ 1 1 1 ]
11. Given the matrix: A = [ 1 0 0 ]
[ 0 2 3 ]
[ 0 4 5 ]
Perform the column operation C2 -> C2 - 2C1 and calculate the new determinant.
12. A = [ 2 0 0 ]
[ 0 3 0 ]
[ 0 0 4 ]
Calculate det(A).
13. For the system of equations:
2x + y = 3
4x + 2y = 6
Use determinants to find the condition for the system to be consistent.
14. A = [ 1 2 3 ]
[ 2 4 5 ]
[ 3 5 6 ]
Calculate det(A).
Whether the student is getting ready for board exams or learning mathematics, they need to practice all these key questions on determinants. Let us see why these questions matter to every student.
Determinants have many advanced concepts in mathematics attached to them. Some of such concepts include matrices, vector algebra, linear transformations, and systems of linear equations. Solving determinant problems will prepare the student for more advanced studies in topics such as:
There are many ways of solving determinant problems. The two most common include cofactor expansion and row and column operations, which require two different approaches and critical thinking to identify patterns and strategies. This enhances your:
This study of determinants and matrices is a crucial part of the syllabus for both Class 12 Mathematics as well as several other competitive exams like:
Determinants are not just theoretical concepts. In reality, determinants have very strong applications. Below are some of the most crucial applications of determinants in any field:
Determinants are one of the key concepts in the Class 12 Mathematics curriculum. When students understand and practice simple concepts that involve the evaluation of determinants, finding inverses of matrices, and their applications to geometric interpretations, they will prepare themselves for exams. With daily practice, students will build confidence and problem-solving ability with these Class 12 Determinants Important questions.
We hope that you practice the above Determinants Class 12 Extra Questions with Solutions and achieve your dream marks.
All the best!
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