NCERT Solutions Exercise 4.4: Determinants

# NCERT Solutions Class 12 Maths Chapter 4 - Determinants

``` Page 1

Question 1:
Find adjoint of each of the matrices.
Question 2:
Find adjoint of each of the matrices.
Page 2

Question 1:
Find adjoint of each of the matrices.
Question 2:
Find adjoint of each of the matrices.
Page 3

Question 1:
Find adjoint of each of the matrices.
Question 2:
Find adjoint of each of the matrices.
Question 3:
Page 4

Question 1:
Find adjoint of each of the matrices.
Question 2:
Find adjoint of each of the matrices.
Question 3:
Question 4:
Page 5

Question 1:
Find adjoint of each of the matrices.
Question 2:
Find adjoint of each of the matrices.
Question 3:
Question 4:
Question 6:
Find the inverse of each of the matrices (if it exists).
```

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

## FAQs on NCERT Solutions Class 12 Maths Chapter 4 - Determinants

 1. What are determinants and why are they important in mathematics?
Ans. Determinants are mathematical objects that are used to solve systems of linear equations, calculate areas and volumes, and determine the invertibility of matrices. They are important because they provide crucial information about the properties and behavior of linear transformations and matrices.
 2. How are determinants calculated for matrices of different dimensions?
Ans. The calculation of determinants depends on the dimensions of the matrix. For 2x2 matrices, the determinant is found by subtracting the product of the diagonal elements from each other. For 3x3 matrices, the determinant can be calculated using a formula involving the cross products of the matrix elements. For higher dimensions, determinants can be calculated recursively using cofactor expansion.
 3. What is the significance of the determinant value?
Ans. The determinant value provides important information about the matrix. If the determinant is zero, it implies that the matrix is not invertible and the system of equations represented by the matrix does not have a unique solution. A non-zero determinant indicates that the matrix is invertible and the system of equations has a unique solution.
 4. How can determinants be used to find the area of a triangle?
Ans. Determinants can be used to find the area of a triangle by considering the coordinates of its vertices. By forming a matrix with the x-coordinates of the vertices in the first column, the y-coordinates in the second column, and a column of ones in the third column, the absolute value of half the determinant of this matrix gives the area of the triangle.
 5. Can determinants be negative?
Ans. Yes, determinants can be negative. The sign of the determinant depends on the arrangement of the elements in the matrix. If the arrangement of the elements leads to an odd number of row exchanges during the calculation of the determinant, the determinant will be negative. If there are an even number of row exchanges, the determinant will be positive.

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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