JEE Advanced Matrix and Determinants Important Questions

Yes, the topic of Matrix and Determinants is extremely important for the candidates who plan on applying for the JEE advanced examinations. In order to boost up the marks in the JEE advanced examination, it is advised that the student be well prepared with all the important topics that this particular chapter holds. There are at least 2-3 questions that are asked from this topic in the JEE advanced question paper. Given below are some important concepts that the student needs to know concerning the topic of Matrix and Determinants.

The term  Matrix is associated with any rectangular arrangement of numbers that are placed in the rows and n columns. It is termed a matrix of order m×n. This is an important formula, as in order to solve any question based on the given topic, this formula needs to be well understood. 

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.

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.