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NCERT Solutions for Class 12 Maths Exercise 4.5 Determinants: The fourth chapter of Class 12 Maths is Determinants. The NCERT Solutions for Class 12 Maths Exercise 4.5 is based on the topic of minors and cofactors. In this section, students study the sub-topic minor in the order of determinants. It is an important topic with a view to understanding Determinants properly Embibe’s solutions guide students on how to simplify the expansion of a determinant in compact form using minors and cofactors.
Embibe provides 300+ practice questions NCERT Maths Class 12 Chapter 4 Exercise 4.5 solutions are designed by academic experts and help students to understand the correct approach to solving all the in-text questions about Determinants. Continue reading this article to know more about Chapter 4 Exercise 4.5 Class 12 Maths.
The NCERT Solutions for Class 12 Maths exercise 4.5 provides sample problems from Embibe to assist students in understanding the correct application of the concepts of minors and cofactors. With the help of Embibe explainers, students can learn the proper application of these concepts and ensure effective exam preparation. The questions are well-researched and crafted to teach students the core concepts.
Also, the NCERT 3D interactive videos provided by Embibe make learning interesting for students, ensuring they can score maximum marks in the board exam. Apart from the video lessons, Embibe provides NCERT Solutions, NCERT Exemplars, Embibe Big Books, mock tests and hundreds of practice questions for.
Students need to only log in to Embibe’s platform and access the excellent study material anytime, anywhere. Below are the important concepts covered under this exercise:
| Sr. No. | Topic |
|---|---|
| 1 | Minors and Cofactors |
| 2 | Find the minor of a given element in a determinant |
| 3 | Find minors and cofactors of all the elements of the determinant |
| 4 | Expanding the given determinant |
| 5 | Solution of System of Linear Equations Using Inverse of a Matrix |
Below are some of the important points students need to remember to score well in the Class 12 board exams:
(i)A square matrix with its determinant is zero is called as a singular matrix.
(ii) Let A=[aij]A=aij be a square matrix of order n(≥2)n≥2 and let BB be a matrix obtained from AA by interchanging any two rows (columns) of AA, then ∣∣B∣∣=−∣∣A∣∣.B=-A.
(iii) If any two rows or columns of a determinant are identical, then its value is zero.
(iv) Let A=[aij]A=aij be a square matrix of order n,n, and let BB be the matrix obtained from AA by multiplying each element of a row (column) of AA by a scalar k,k, then ∣∣B∣∣=k∣∣A∣∣.B=kA.
(v) If A=[aij]A=aij be a square matrix of order nn, then ∣∣kA∣∣=kn∣∣A∣∣.kA=knA.
(vi) If each element of a row (column) of a determinant is expressed as a sum of two or more terms, then the determinant can be expressed as the sum of two or more determinants.
(vii) If each element of a row (column) of a determinant is multiplied by the same constant and then added to the corresponding elements of some other row (column), then the value of the determinant remains the same.
(viii) If each element of a row (column) of a determinant is zero, then its value is zero.
Below are the direct links to NCERT Solutions for Class 12 Maths other chapters:
Ans: Embibe provides 300+ practice questions on the topic Minors and Cofactors in Class 12 Maths Chapter 4 exercise 4.5. Students can visit the website or download the app and start solving them at their convenience.
Ans: Yes, the NCERT Solutions for Class 12 Maths chapter 4 can be accessed for on Embibe.
Ans: Solving the NCERT Solutions Class 12 Maths exercise 4.5 will help students in building a solid foundation in the topic and solve different kinds of questions based on it.
Ans: The NCERT notes, videos and books offered by Embibe follow the latest CBSE guidelines and are undoubtedly the best study material for exam preparations.
Ans: Yes, Embibe’s 3D video lessons for Class 12 Maths exercise 4.5 are for. Students just need to log in to the platform and start practicing.
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