# CBSE Class 12 Mathematics NCERT Exemplar Solutions: Chapter - Determinants

Jul 11, 2018 17:40 IST CBSE Class 12 Mathematics NCERT Exemplar Solutions

In this article, we are providing you NCERT Exemplar Solutions for all the questions of Class 12 Mathematics Chapter 4 – Determinants. Questions from NCERT Exemplar are frequently asked in CBSE Class 12 Board examination and various engineering entrance examinations like JEE Main, JEE Advanced, WBJEEE, AIPMT etc.

## Important Topics of Chapter – Determinants

• Determinant of a square matrix (up to 3 × 3 matrices)
• Properties of determinants
• Adjoint and inverse of a square matrix
• Consistency, inconsistency and number of solutions of system of linear equations
• Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

## About NCERT Exemplar Solutions Class 12 Maths:

Students must go through the basic concepts before checking the solutions given here. All the solutions of the chapter Determinants are solved by subject experts of Mathematics. Students can easily understand all the solutions as all the steps are included while solving questions.

Few problems along with their solutions from this chapter are given follows:

Question:

If the area of a triangle with vertices (- 3, 0), (3, 0) and (0, k) is 9 sq units. Then, the value of k will be

(a) 9

(b) 3

(c) -9

(d) 6

Solution: (b) Question:

If A is a matrix of order 3 × 3, then (A2)-1 is equal to ........  .

Solution:

We know that, (An)-1 = (A-1)n, where nN.

Substituting n = 2 on both sides, we get

(A2)-1 = (A-1)2

Question:

If A is a matrix of order 3 × 3, then the number of minors in determinant of A are ........  .

Solution:

Since, the order of the matrix A is 3 × 3. It means there are 9 elements in the matrix A.

Hence, the number of minors in determinant of A is 9.

Question:

The sum of products of elements of any row with the cofactors of corresponding elements is equal to ........  .

Solution: = Sum of products of elements of R1 with their corresponding cofactors.

Hence, the sum of products of elements of any row with the cofactors of corresponding elements is equal to value of the determinant.

Students can download the complete solutions in PDF form using the links given below: