JEE Advanced Matrix and Determinants Important Questions

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.

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Next Steps: Further Resources for Important Questions of JEE Advanced 2025 Matrix and Determinants

Explore additional resources beyond JEE Advanced 2025 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.

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Maths Important Questions for JEE Advanced 2025 Chapters: Links Available

Make your JEE Advanced Maths studying for 2025 even better using our Important Questions organised by chapter. Find the links in the table below for easy access.

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.