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JEE Advanced Matrix and Determinants Important Questions

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Last updated date: 28th May 2024
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JEE Advanced Maths Matrix and Determinants Important Questions from PYQs with Solutions

One of the most scoring Maths chapters in JEE Advanced is Matrix and Determinants. A Matrix is a set of numbers, generally, for JEE Advanced, matrices may be referred to as 2D arrays. Some aspirants find square matrices easier to solve for. This chapter has sums to calculate the determinant of matrices. Vedantu provides a helpful resource for JEE Advanced 2024 students. It includes carefully chosen Matrix and Determinants Important Questions, made by Vedantu's expert teachers. These questions match the JEE Advanced exam syllabus and come in multiple-choice and solving formats. They come with detailed solutions to help students understand the methods. The resource also includes previous year questions from JEE Advanced exams, all available for free in PDF format on Vedantu's website.

Category:

JEE Advanced Important Questions

Content-Type:

Text, Images, Videos and PDF

Exam:

JEE Advanced

Chapter Name:

Matrix and Determinants

Academic Session:

2024

Medium:

English Medium

Subject:

Mathematics

Available Material:

Chapter-wise Important Questions with PDF

Secure a Top Score in Your JEE Advanced Maths Matrix and Determinants Exam with Our Practice Papers

Don't miss your chance to ace your JEE Advanced Maths Matrix and Determinants exam. Download our JEE Advanced Maths Matrix and Determinants practice paper today and start practicing! With targeted questions and in-depth solutions, you'll be well on your way to success.

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JEE Advanced Important Questions of Matrix and Determinants

One of the most scoring Maths chapters in JEE Advanced is Matrix and Determinants. A Matrix is a set of numbers, generally, for JEE Advanced, matrices may be referred to as 2D arrays. Some aspirants find square matrices easier to solve for. This chapter has sums to calculate the determinant of matrices. The important questions on Matrix and Determinants for JEE Advanced along with their solutions are provided in the below PDF. These sums have been solved by subject matter experts at Vedantu.


JEE Advanced Matrix and Determinants Important Questions part-1


Matrix and Determinants Important Questions for JEE Advanced


For a square matrix having four terms, the determinant can be calculated as follows:


  • IAI = Product of the first and third terms - Product of the second and fourth terms. 

  • (IAI is used to denote the determinant value of any matrix)


Another common question that comes from Matrix and Determinants, is finding the inverse of a matrix. A-1 is used to denote the inverse of a Matrix. If the original matrix is multiplied by the inverse of the matrix, then the resultant matrix is an identity matrix. The diagonal elements of an Identity Matrix are 1’s whereas the rest of the elements are all zeros. JEE Advanced Matrix and Determinant Important Questions and their solutions are provided in the below PDF, which can be downloaded for free.


A x A - 1 = I


Some of the common operations on matrices are addition, subtraction, multiplication, and division. Among all these, the multiplication of matrices can be a little tricky when they are not nxn matrices. If the matrices are having different dimensions, then the resulting matrix has the following dimensions:


  • The no. of rows of the resultant matrix = the number of rows of the first matrix

  • The no. of columns of the resultant matrix = the number of columns of the second matrix.


Formulaic Support: Boosting Understanding with  JEE Advanced Matrix and Determinants Important Questions

If you are aiming for effective learning, consider employing a strategic approach that integrates Matrix and Determinants important questions for JEE Advanced with essential formulas and crucial questions, There are at least 2-3 questions that are asked from this topic in the JEE Advanced question paper. Formulas serve as concise explanations of fundamental concepts, while solved questions provide a comprehensive learning experience. A strong foundation is established through JEE Advanced Matrix and Determinants Important Questions, and formulas aid in comprehending concepts and addressing problems. This fusion streamlines complex topics and enhances memory retention, ultimately boosting your comprehension and academic performance.


Basic Definitions

  • The matrix that has only one row is termed the row matrix. 

  • A matrix consisting of only one column is called a column matrix. 

  • A matrix that is placed in the order of order m×n is called the square matrix provided that m = n.

  • When  A = (aij)m×n,  it is called a zero matrix, provided that aij = 0 for all i and j.

  • When A = (aij)m×n then it is termed as the upper triangular, but on a condition where if aij= 0 for i > j.

  • When  A = (aij)m×n , then it is considered to be a  lower triangular matrix, only if aij = 0 for i < j.

  •  A square matrix (aij)m×n is also termed as a diagonal matrix, where aij = 0 for i ≠ j.

  • When a diagonal matrix A = (aij)m×n, then it is said to be a scalar matrix, provided that for aij = k for i = j.

  • Unit matrix (Identity matrix): when a diagonal matrix A = (aij)n , then it is referred to as a unit matrix or an identity matrix, given that aij = 1 for i = j.

  • If they have the same order then the given Matrices A and B are said to be comparable.


Most Important Formulas of Matrix and Determinants for JEE Advanced

1. Quadratic Formula:

  • $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$


2. Nature of Roots:

  • If $b^2 - 4ac > 0$, the roots are real and distinct.

  • If $b^2 - 4ac = 0$, the roots are real and equal.

  • If $b^2 - 4ac < 0$, the roots are complex conjugates.


3. Sum and Product of Roots:

  • Sum of roots, $\alpha + \beta = -\frac{b}{a}$

  • Product of roots, $\alpha \cdot \beta = \frac{c}{a}$


4. Quadratic Equation in Vertex Form:

  • $y = a(x - h)^2 + k$, where (h,k) is the vertex of the parabola.


5. Nature of Quadratic Expression:

  • If a > 0, the parabola opens upwards, and the vertex is the minimum point.

  • If a < 0, the parabola opens downwards, and the vertex is the maximum point.


Download Vedantu's  Maths Formulas, including the Matrix and Determinants important questions JEE Advanced, completely FREE. Combine these resources with JEE Advanced Important Questions, and you'll undoubtedly observe significant improvements in your scores.


Next Steps: Further Resources for Important Questions of JEE Advanced 2024 Matrix and Determinants

Explore additional resources beyond JEE Advanced 2024 Matrix and Determinants Important Questions. Students need to consider extra materials like practice papers, mock tests, PYQPs, etc., alongside important Matrix and Determinants questions to gain a well-rounded preparation, refine their exam strategies, and build confidence for the JEE Advanced exam.


Ready to take your JEE Advanced 2024 Matrix and Determinants preparation up a notch? Delve into these crucial resources:




Maths Important Questions for JEE Advanced 2024 Chapters: Links Available

Make your JEE Advanced Maths studying for 2024 even better using our Important Questions organised by chapter. Find the links in the table below for easy access.


JEE Advanced 2024: Chapter-Wise Links to Maths Important Questions PDF

S.No

Chapter Name

1

Sets, Relations and Functions

2

Algebra

3

Matrices

4

Probability and Statistics 

5

Trigonometry

6

Analytical Geometry 

7

Differential Calculus 

8

Integral Calculus 

9

Vectors



Get Ahead in your Exams with Vedantu’s JEE Advanced Matrix and Determinants Important Questions

Questions from the chapter Matrix and Determinants are important for JEE Advanced. Fascinating mathematical concepts that play a crucial role in solving various problem questions in JEE Advanced and other exams. Through the JEE Advanced Matrix and Determinants Important Questions PDF provided by Vedantu, we have delved into the intricate world of Matrix and Determinants, exploring their properties and applications. JEE Advanced Matrix and Determinants Important Questions offer valuable insights, helping us grasp the fundamental principles and solving techniques for exams. With a deeper understanding of these topics, we can approach mathematical challenges with confidence and creativity, paving the way for success in both academic and practical endeavours. So, keep exploring, solving, and embracing the beauty of Matrix and Determinants on your mathematical journey.

FAQs on JEE Advanced Matrix and Determinants Important Questions

1. How many questions are asked from matrices and determinants in JEE Advanced exam?

Based on past trends and the importance of the topic, experts estimate that there are usually 2-3 questions on this topic.  So it's a good idea to be thorough in your understanding of matrices and determinants.

2. What are the 4 types of matrices?

There are actually more than four types of matrices, but some common ones include:


  1. Square Matrix: Same number of rows and columns.

  2. Diagonal Matrix: Only entries on the main diagonal are non-zero.

  3. Identity Matrix: Square matrix with 1s on the diagonal and 0s elsewhere.

  4. Zero Matrix: All entries are zero.

3. What are the 5 matrix rules?

There are many matrix rules, but some basic ones include:


  1. Addition/Subtraction: Only possible for matrices with the same dimensions.

  2. Scalar multiplication: Multiplying each term of the matrix by a number.

  3. Matrix multiplication: Specific operation for multiplying two matrices.

  4. Transpose: Swapping rows and columns.

  5. Inverse: Only square matrices have inverses, and it "undoes" the matrix multiplication.

4. Where can we get the Matrix and Determinants Important questions for the JEE advanced exams?

Students can get access to Matrix and Determinants important questions from the website of Vedantu. The student can visit the website and download the PDF for free. The PDF is updated regularly and will help the student immensely in the preparation of their examination. Practicing these questions will help the student understand the important topics and realize the areas they might need to improve. Apart from this, it also helps the students to learn the practice of time management. Practicing the questions will help the student to understand the ways in which the questions are to be answered while also saving time for revision. 

5. Are Matrices and Determinants hard for the JEE Advanced examinations?

No, the topic Matrices and Determiners is not hard for the JEE advanced examinations. It is the easiest topic where the candidate can score marks easily. But to achieve this, it is important that the student be thorough with all the little details that this chapter has to offer. Though this topic is not the hardest and time-consuming, it still is the most important topic for the exam. And in order to master this topic, the student needs to practice all the tricks that will help them solve the questions easily in the exam. To help the students achieve this, the website of vedantu provides the students with all the important questions and study materials that will help the students focus on the important areas of the given topic.

6. What is the relation between matrix and determinant?

  • A matrix is a rectangular array of numbers, while a determinant is a single number calculated from a square matrix (a matrix with the same number of rows and columns). (In short: Matrices are the source, determinants are the extract)


  • The determinant captures certain properties of a square matrix, such as invertibility or the scaling effect of linear transformations represented by the matrix.


  • Not all matrices have determinants: Determinants can only be calculated for square matrices. Rectangular matrices (with different numbers of rows and columns) don't have determinants.


  • The value of the determinant is useful in various matrix operations like finding the inverse of a matrix, solving systems of linear equations (Cramer's rule), and analyzing areas/volumes in linear algebra.

7. Is zero matrix a scalar matrix?

No. A scalar matrix is a diagonal matrix where all the diagonal entries are the same number (not necessarily zero).  A zero matrix has all entries as zero.

8. What does a T mean in matrices?

In most cases, "T" refers to the transpose of a matrix. It swaps the rows and columns.

9. What is matrix in real life?

Matrices are used extensively in various fields. Here are some examples:


  • Data Analysis: Matrices can store and organize large datasets for analysis in statistics, economics, and social sciences.

  • Computer Graphics: They represent 3D objects, transformations, and lighting effects in video games and animation.

  • Cryptography: Encryption algorithms use matrices to scramble and unscramble data.

  • Physics and Engineering: Matrices describe forces, solve equations in mechanics, and model electrical circuits.