NCERT Exemplar Class 12 Maths Chapter 4 Solutions: Determinants
NCERT Exemplar Class 12 Maths Solutions Chapter 4 ‘Determinants’ are designed to help you for the Central Board of Secondary Education examination. There are 58 exemplar problems and solutions in this chapter of NCERT Exemplar Class 12 Maths. There is always a chance of 8-10 marks questions in the final examination related to this chapter. So refer to our solutions and prepare the chapter well before the exams.
With the help of NCERT Exemplar problems for Class 12 Maths Chapter 4, we shall learn about the definitions of determinants, the determinant of a matrix of order one, order two and order 3*3, its properties, inverse and adjoint of the matrix, application of matrices and determinants. The exemplar problems are framed in such a way that you can understand thoroughly and apply the concept wherever required.
Important Topics for NCERT Maths Exemplar Solutions Class 12 Chapters 4
- Determinants: These are used for the solutions of linear equations. According to the rule of Cramer, any different type of linear equations have an exceptional answer if and only if the matrix‘s determinant is not zero.
Removing X, Y, and Z from the given equation below:
A_{1}X +A_{2}Y+A_{3}Z =0 (1)
B_{1}X+B_{2}Y+B_{3}Z =0 (2)
C_{1}X+C_{2}Y+C_{3}Z=0 (3)
With the help of 1, 2, 3 the expressions come:
A_{1} B_{2} C_{3} – A_{1} B_{3} C_{2}+ A_{2} B_{3} C_{1}– A_{2} B_{1} C_{3} + A_{3} B_{1} C_{2} – A_{3} B_{2} C_{1} = ZERO,
It is called the determinant for this particular equation. We can only define the determinants for a square matrix.
- Properties of determinant:
- 1. If you switch any two rows/ columns, it will change the sign
- There is no need to change the value of determinants, one can simply add the multiples of rows and columns,
- Any determinant having zeros in their row/columns has value zero.
- There will be no difference in the determinant if columns are changed to rows and
Vice versa.
- Element of row / column =zero , then determinant = zero
- Property of the sum
- Invariance Property
Minors of the element:
It is obtained by subtracting the particular row and column in which the component lies.
For example:
D= b_{11} b_{12} b_{13}
b_{21} b_{22} b_{23}
b_{31} b_{32 }b_{33}
Then minors of
b12 = M12 = b_{21} b_{23} b_{31 }b_{33}
- Solving the linear equation with the help of determinants
- Involving two variables with the help of determinants
- Involving three variables with the help of determinants.
Exercise Discussion of NCERT Maths Exemplar Solutions Class 12 Chapter 4
- The first 10 NCERT Exemplar problems for Class 12 Maths Chapter 4 are related to the matrix, solving the question by opening the matrix and applying certain properties of determinants. These questions are short in length and do not require many calculations.
- In the next 8 exemplar problems, it is a mixture of objective type questions and true/false types. Where after solving the determinant of the element, the answer is given.
- The next exercise demands the use of properties of determinants and its right application. It has 6 questions for the same. There are some questions based on the area of the triangle, where the length of ‘a’ is asked. A mixture of questions based on the value of theta, x, question-related to AP and GP. Are also asked.
- The next series of exemplar problems include the long answer type questions, where certain equations are given to form the matrix with the help of the matrix method and vice versa. These types of questions are very lengthy in nature and are time-consuming. A student needs to have a thorough practise of such types of questions to gain good marks. Generally, students fail to attempt such a question due to non-clarity of concept, properties, and shortcuts.
Why Use NCERT Maths Exemplar Solutions Class 12 Chapter 4 by Instasolv?
NCERT Exemplar Class 12 Maths Solutions Chapter 4 are very useful preparation of exams for state boards, ICSE board, JEE mains, JEE Advanced, NEET and other competitive examinations. Solving exemplar problems would develop your aptitude skills for the unfathomable understanding of this subject. Instasolv’s Exemplar Solutions for chapter 4 Determinants are available online at no cost for you. So access them any time and begin your preparations for the exams.