Open App

JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations

RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations | Mathematics (Maths) Class 12 - JEE PDF Download

Download, print and study this document offline

Please wait while the PDF view is loading

 Page 1


8. Solution of Simultaneous Linear Equations
Exercise 8.1
1 A. Question
Solve the following system of equations by matrix method:
5x + 7y + 2 = 0
4x + 6y + 3 = 0
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 30 – 28 = 2
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 6 = 6
C
12
 = (– 1)
1 + 2
 4 = – 4
C
21
 = (– 1)
2 + 1
 7 = – 7
C
22
 = (– 1)
2 + 2
 5 = 5
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X =  Y = 
1 B. Question
Solve the following system of equations by matrix method:
Page 2


8. Solution of Simultaneous Linear Equations
Exercise 8.1
1 A. Question
Solve the following system of equations by matrix method:
5x + 7y + 2 = 0
4x + 6y + 3 = 0
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 30 – 28 = 2
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 6 = 6
C
12
 = (– 1)
1 + 2
 4 = – 4
C
21
 = (– 1)
2 + 1
 7 = – 7
C
22
 = (– 1)
2 + 2
 5 = 5
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X =  Y = 
1 B. Question
Solve the following system of equations by matrix method:
5x + 2y = 3
3x + 2y = 5
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 10 – 6 = 4
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 2 = 2
C
12
 = (– 1)
1 + 2
 3 = – 3
C
21
 = (– 1)
2 + 1
 2 = – 2
C
22
 = (– 1)
2 + 2
 2 = 5
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X =  Y = 4
1 C. Question
Solve the following system of equations by matrix method:
3x + 4y = 5
x – y = – 3
Answer
The above system of equations can be written as
Page 3


8. Solution of Simultaneous Linear Equations
Exercise 8.1
1 A. Question
Solve the following system of equations by matrix method:
5x + 7y + 2 = 0
4x + 6y + 3 = 0
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 30 – 28 = 2
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 6 = 6
C
12
 = (– 1)
1 + 2
 4 = – 4
C
21
 = (– 1)
2 + 1
 7 = – 7
C
22
 = (– 1)
2 + 2
 5 = 5
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X =  Y = 
1 B. Question
Solve the following system of equations by matrix method:
5x + 2y = 3
3x + 2y = 5
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 10 – 6 = 4
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 2 = 2
C
12
 = (– 1)
1 + 2
 3 = – 3
C
21
 = (– 1)
2 + 1
 2 = – 2
C
22
 = (– 1)
2 + 2
 2 = 5
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X =  Y = 4
1 C. Question
Solve the following system of equations by matrix method:
3x + 4y = 5
x – y = – 3
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = – 3 – 4 = – 7
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 – 1 = – 1
C
12
 = (– 1)
1 + 2
 1 = – 1
C
21
 = (– 1)
2 + 1
 4 = – 4
C
22
 = (– 1)
2 + 2
 3 = 3
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X = 1 Y = – 2
1 D. Question
Solve the following system of equations by matrix method:
3x + y = 19
3x – y = 23
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = – 3 – 3 = – 6
Page 4


8. Solution of Simultaneous Linear Equations
Exercise 8.1
1 A. Question
Solve the following system of equations by matrix method:
5x + 7y + 2 = 0
4x + 6y + 3 = 0
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 30 – 28 = 2
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 6 = 6
C
12
 = (– 1)
1 + 2
 4 = – 4
C
21
 = (– 1)
2 + 1
 7 = – 7
C
22
 = (– 1)
2 + 2
 5 = 5
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X =  Y = 
1 B. Question
Solve the following system of equations by matrix method:
5x + 2y = 3
3x + 2y = 5
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 10 – 6 = 4
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 2 = 2
C
12
 = (– 1)
1 + 2
 3 = – 3
C
21
 = (– 1)
2 + 1
 2 = – 2
C
22
 = (– 1)
2 + 2
 2 = 5
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X =  Y = 4
1 C. Question
Solve the following system of equations by matrix method:
3x + 4y = 5
x – y = – 3
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = – 3 – 4 = – 7
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 – 1 = – 1
C
12
 = (– 1)
1 + 2
 1 = – 1
C
21
 = (– 1)
2 + 1
 4 = – 4
C
22
 = (– 1)
2 + 2
 3 = 3
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X = 1 Y = – 2
1 D. Question
Solve the following system of equations by matrix method:
3x + y = 19
3x – y = 23
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = – 3 – 3 = – 6
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 – 1 = – 1
C
12
 = (– 1)
1 + 2
 3 = – 3
C
21
 = (– 1)
2 + 1
 1 = – 1
C
22
 = (– 1)
2 + 2
 3 = 3
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X = 7 Y = – 2
1 E. Question
Solve the following system of equations by matrix method:
3x + 7y = 4
x + 2y = – 1
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 6 – 7 = – 1
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 2 = 2
Page 5


8. Solution of Simultaneous Linear Equations
Exercise 8.1
1 A. Question
Solve the following system of equations by matrix method:
5x + 7y + 2 = 0
4x + 6y + 3 = 0
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 30 – 28 = 2
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 6 = 6
C
12
 = (– 1)
1 + 2
 4 = – 4
C
21
 = (– 1)
2 + 1
 7 = – 7
C
22
 = (– 1)
2 + 2
 5 = 5
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X =  Y = 
1 B. Question
Solve the following system of equations by matrix method:
5x + 2y = 3
3x + 2y = 5
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 10 – 6 = 4
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 2 = 2
C
12
 = (– 1)
1 + 2
 3 = – 3
C
21
 = (– 1)
2 + 1
 2 = – 2
C
22
 = (– 1)
2 + 2
 2 = 5
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X =  Y = 4
1 C. Question
Solve the following system of equations by matrix method:
3x + 4y = 5
x – y = – 3
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = – 3 – 4 = – 7
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 – 1 = – 1
C
12
 = (– 1)
1 + 2
 1 = – 1
C
21
 = (– 1)
2 + 1
 4 = – 4
C
22
 = (– 1)
2 + 2
 3 = 3
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X = 1 Y = – 2
1 D. Question
Solve the following system of equations by matrix method:
3x + y = 19
3x – y = 23
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = – 3 – 3 = – 6
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 – 1 = – 1
C
12
 = (– 1)
1 + 2
 3 = – 3
C
21
 = (– 1)
2 + 1
 1 = – 1
C
22
 = (– 1)
2 + 2
 3 = 3
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X = 7 Y = – 2
1 E. Question
Solve the following system of equations by matrix method:
3x + 7y = 4
x + 2y = – 1
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 6 – 7 = – 1
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 2 = 2
C
12
 = (– 1)
1 + 2
 1 = – 1
C
21
 = (– 1)
2 + 1
 7 = – 7
C
22
 = (– 1)
2 + 2
 3 = 3
Also, adj A = 
= 
A 
– 1
 = 
A 
– 1
 = 
Now, X = A 
– 1
B
Hence, X = – 15 Y = 7
1 F. Question
Solve the following system of equations by matrix method:
3x + y = 7
5x + 3y = 12
Answer
The above system of equations can be written as
 or AX = B
Where A =  B =  and X = 
|A| = 9 – 5 = 4
So, the above system has a unique solution, given by
X = A 
– 1
B
Let C
ij
 be the cofactor of a
ij
in A, then
C
11
 = (– 1)
1 + 1
 3 = 3
C
12
 = (– 1)
1 + 2
 5 = – 5
C
21
 = (– 1)
2 + 1
 1 = – 1
C
22
 = (– 1)
2 + 2
 3 = 3

	Mathematics (Maths) Class 12 204 videos\|290 docs\|139 tests

Mathematics (Maths) Class 12

204 videos|290 docs|139 tests

Join Course for Free

Top Courses for JEE

View all

Related Exams

JEE Commerce Humanities/Arts Class 12 Class 11 Grade 12

About this Document

Dec 22, 2024 Last updated

Document Description: RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The notes and questions for RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations have been prepared according to the JEE exam syllabus. Information about RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations covers topics like and RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations.

Introduction of RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations in English is available as part of our Mathematics (Maths) Class 12 for JEE & RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations in Hindi for Mathematics (Maths) Class 12 course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations | Mathematics (Maths) Class 12 - JEE

Description

Full syllabus notes, lecture & questions for RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations | Mathematics (Maths) Class 12 - JEE - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 12 | Best notes, free PDF download

Information about RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations

In this doc you can find the meaning of RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations defined & explained in the simplest way possible. Besides explaining types of RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations theory, EduRev gives you an ample number of questions to practice RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations tests, examples and also practice JEE tests

	Mathematics (Maths) Class 12 204 videos\|290 docs\|139 tests

Mathematics (Maths) Class 12

204 videos|290 docs|139 tests

Join Course for Free

Download as PDF

Explore Courses for JEE exam

Top Courses for JEE

Explore Courses

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

study material

Important questions

Exam

ppt

RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations | Mathematics (Maths) Class 12 - JEE

shortcuts and tricks

Semester Notes

Summary

Objective type Questions

Viva Questions

MCQs

video lectures

mock tests for examination

Previous Year Questions with Solutions

RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations | Mathematics (Maths) Class 12 - JEE

practice quizzes

Sample Paper

Extra Questions

Free

pdf

past year papers

;

Additional Information about RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations for JEE Preparation

RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations Free PDF Download

The RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations is an invaluable resource that delves deep into the core of the JEE exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations now and kickstart your journey towards success in the JEE exam.

Importance of RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations

The importance of RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations cannot be overstated, especially for JEE aspirants. This document holds the key to success in the JEE exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations Notes

RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations Notes on EduRev are your ultimate resource for success.

RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations JEE Questions

The "RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations JEE Questions" guide is a valuable resource for all aspiring students preparing for the JEE exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations on the App

Students of JEE can study RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of RD Sharma Class 12 Solutions - Solution of Simultaneous Linear Equations is prepared as per the latest JEE syllabus.

Education Revolution