Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices

Class 11: Maths Chapter 4 solutions. Complete Class 11 Maths Chapter 4 Notes.

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices

Maharashtra Board 11th Maths Chapter 4, Class 11 Maths Chapter 4 solutions

Ex 4.1

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.1

Ex 4.2

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2

∴ x — 1 = 0 or x-2 = 0 or x-3 = 0
∴ x = 1 or x = 2 or x = 3

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.2

Ex 4.3

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3

= 0
∴ The given equations are consistent.

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3

∴ k(-1) – 3(-1) + 1(-1) = 0
∴ -k + 3 – 1 = 0
∴ k = 2.

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.3

Ex 4.4

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.4

Ex 4.5

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5

three subjects – Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B.

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5

i. Find the increase in sales in Rupees from July to August 2017.
ii. If both book shops got 10% profit in the month of August 2017, find the profit for each bookseller in each subject in that month.
Solution:

i. Increase in sales in rupees from July to August 2017
For Suresh:
Increase in sales for Physics books
= 6650 – 5600= ₹ 1050
Increase in sales for Chemistry books
= 7055 – 6750 = ₹ 305
Increase in sales for Mathematics books
= 8905 – 8500 = ₹ 405
For Ganesh:
Increase in sales for Physics books
= 7000 – 6650 = ₹ 350
Increase in sales for Chemistry books
= 7500 – 7055 = ₹ 445
Increase in sales for Mathematics books
= 10200 – 8905 = ₹ 1295
[Note: Answers given in the textbook are 1760, 2090. However, as per our calculation they are 1050, 305, 405, 350, 445, 1295.]

ii. Both book shops got 10% profit in the month of August 2017.
For Suresh:

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.5

Ex 4.6

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6

From (i) and (ii), we get
AB = BA

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.6

Ex 4.7

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7

∴ A is a diagonal matrix.

Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7
Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices Ex 4.7

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Maharashtra Board Solutions Class 11-Arts & Science Maths (Part 1): Chapter 4- Determinants and Matrices

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Chapterwise Maharashtra Board Solutions Class 11 Arts & Science Maths (Part 1) :

FAQs

Where do I get the Maharashtra State Board Books PDF For free download?

You can download the Maharashtra State Board Books from the eBalbharti official website, i.e. cart.ebalbharati.in or from this article.

How to Download Maharashtra State Board Books?

Students can get the Maharashtra Books for primary, secondary, and senior secondary classes from here.  You can view or download the Maharashtra State Board Books from this page or from the official website for free of cost. Students can follow the detailed steps below to visit the official website and download the e-books for all subjects or a specific subject in different mediums.
Step 1: Visit the official website ebalbharati.in
Step 2: On the top of the screen, select “Download PDF textbooks” 
Step 3: From the “Classes” section, select your class.
Step 4: From “Medium”, select the medium suitable to you.
Step 5: All Maharashtra board books for your class will now be displayed on the right side. 
Step 6: Click on the “Download” option to download the PDF book.

Who developed the Maharashtra State board books?

As of now, the MSCERT and Balbharti are responsible for the syllabus and textbooks of Classes 1 to 8, while Classes 9 and 10 are under the Maharashtra State Board of Secondary and Higher Secondary Education (MSBSHSE).

How many state boards are there in Maharashtra?

The Maharashtra State Board of Secondary & Higher Secondary Education, conducts the HSC and SSC Examinations in the state of Maharashtra through its nine Divisional Boards located at Pune, Mumbai, Aurangabad, Nasik, Kolhapur, Amravati, Latur, Nagpur and Ratnagiri.

About Maharashtra State Board (MSBSHSE)

The Maharashtra State Board of Secondary and Higher Secondary Education or MSBSHSE (Marathi: महाराष्ट्र राज्य माध्यमिक आणि उच्च माध्यमिक शिक्षण मंडळ), is an autonomous and statutory body established in 1965. The board was amended in the year 1977 under the provisions of the Maharashtra Act No. 41 of 1965.

The Maharashtra State Board of Secondary & Higher Secondary Education (MSBSHSE), Pune is an independent body of the Maharashtra Government. There are more than 1.4 million students that appear in the examination every year. The Maha State Board conducts the board examination twice a year. This board conducts the examination for SSC and HSC. 

The Maharashtra government established the Maharashtra State Bureau of Textbook Production and Curriculum Research, also commonly referred to as Ebalbharati, in 1967 to take up the responsibility of providing quality textbooks to students from all classes studying under the Maharashtra State Board. MSBHSE prepares and updates the curriculum to provide holistic development for students. It is designed to tackle the difficulty in understanding the concepts with simple language with simple illustrations. Every year around 10 lakh students are enrolled in schools that are affiliated with the Maharashtra State Board.

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