NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5: NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5, comprises solutions of questions of Exercise 4.5. Subject experts have designed these NCERT Solutions for Class 12 Maths easily and simply.
Students can understand the concepts without any hassle. To understand the NCERT Solutions of Class 12 mathematics and excel in their maths skills, you can download its PDF.
NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5
NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5 pdf
Download NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5 PDF:
NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5
For scoring good marks, you must have a good understanding of the concepts. This can be made possible when you are strengthening your concepts from the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5. High-quality content designed by subject matter experts just for clearing your doubts.
There are many important topics as well as sub-topics that are crucial for your class 12 board exams. NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5 is available in PDF form for Free and you can download it any time you want.
All the topics covered in this chapter are mentioned in the list below:
- Definition of Determinants
- Application of Determinants
- Types of Determinants
- Properties of Determinants
- Area of a triangle
- Minors & Co-factors
- Adjoint & Inverse of a matrix
- Singular & Non-Singular Matrix
- Applications of Determinants and Matrices
- Solution of a System of Linear Equations using Inverse of a matrix
Types of Determinants
There are three types of Determinants:
- First-order determinant: The determinant of the matrix of first-order is said to be the element itself. If A = [a], matrix of order 1, Determinant of A is said to be equivalent of a.
- Second-order determinant: In the case of Determinant of matrices order 2, Determinant is obtained by multiplying the matrices.
- Third-order determinant: In the case of Determinant of matrices order 3 x 3, Determinant is obtained through a series of steps, explained in a detailed manner in the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5.
Properties of Determinants
Here are various properties of Determinants explained in the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5.
- Property 1: The value of the determinant will remain unchanged when two rows or two columns are interchanged.
- Property 2: The value of the determinant will change the concerning sign whenever two rows or two columns are interchanged.
- Property 3: The value of the determinant will remain zero when two rows or two columns are the same.
- Property 4: If each element in a matrix is multiplied by a constant, ‘k’, the value of the determinant will be multiplied by k, as well.
- Property 5: If the sum of two terms is expressing elements, the value of the determinant will be expressed by the sum.
- Property 6: An element of any row or column of a determinant, the equimultiples of the corresponding elements of other row or column are added, the value of the determinant remains if the operation is applied.
- Property 7: If all the determinants on one side of the principle diagonal are zero, the value of the determinant is equal to the product of the elements in the principle diagonal.
Adjoint & Inverse of a matrix
Theorem 1: When a is any given Square matrix of order ‘n’, then A(adj A) = (adjA)A = AI
Singular & Non-Singular Matrix
Theorem 2: If A & B are non-singular matrices of a similar order, then AB & BA are the non-singular matrices of a similar order.
Theorem 3: The determinant of the product of matrices is equivalent to the product to their determinants respectively. AB = |A| |B|, where A & B are Square matrices of a similar order.
Theorem 4: When A is a non-singular matrix, only then a square matrix A is invertible.
Access Other Exercise NCERT Solutions of Class 12 Maths Determinants
You can download the PDF of NCERT Solutions CBSE Class 12 Maths for Chapter 4 other exercise:
- Exercise 4.1
- Exercise 4.2
- Exercise 4.3
- Exercise 4.4
All the best to the students appearing for the Class 12th board exam. Here is the detailed blog of NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5. For further queries regarding the Class 12th exam, you can ask in the comment box.
FAQs on the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5
How much does it cost to download the NCERT Solutions of Class 12 Maths Determinants PDF?
It is free of cost. You don’t have to pay for downloading the PDFs.
State the Determinant of matrices order 1.
Determinant of matrices order 1:
If A = [a], matrix of order 1, Determinant of A is said to be equivalent of a.
State the Determinant of matrices order 3 x 3.
In the case of Determinant of matrices order 3 x 3, Determinant is obtained through a series of steps.
From where can I download the NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5 Free PDF?
You can download it from Kopykitab.
Why should we study from NCERT Solutions Class 12 Maths Chapter 4 Exercise 4.5?
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What are some of the properties of a determinant?
The properties of a determinant are:
All-Zero property
Reflection Property
Scalar Multiple Property, and more