JEE Exam  >  JEE Notes  >  Mathematics (Maths) Class 12  >  RD Sharma Class 12 Solutions - Adjoint and Inverse of a Matrix

RD Sharma Class 12 Solutions - Adjoint and Inverse of a Matrix | Mathematics (Maths) Class 12 - JEE PDF Download

Download, print and study this document offline
Please wait while the PDF view is loading
 Page 1


7. Adjoint and Inverse of a Matrix
Exercise 7.1
1 A. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 4
C
12
 = – 2
C
21
 = – 5
C
22
 = – 3
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
Also, A(adj A) = 
A(adj A) = 
Hence, (adj A)A = |A|.I = A.(adj A)
1 B. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Page 2


7. Adjoint and Inverse of a Matrix
Exercise 7.1
1 A. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 4
C
12
 = – 2
C
21
 = – 5
C
22
 = – 3
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
Also, A(adj A) = 
A(adj A) = 
Hence, (adj A)A = |A|.I = A.(adj A)
1 B. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = d
C
12
 = – c
C
21
 = – b
C
22
 = a
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
Also, A(adj A) = 
Hence, (adj A)A = |A|.I = A.(adj A)
1 C. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 
C
12
 = 
C
21
 = 
C
22
 = 
Since, adj A = 
(adj A) = 
= 
Page 3


7. Adjoint and Inverse of a Matrix
Exercise 7.1
1 A. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 4
C
12
 = – 2
C
21
 = – 5
C
22
 = – 3
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
Also, A(adj A) = 
A(adj A) = 
Hence, (adj A)A = |A|.I = A.(adj A)
1 B. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = d
C
12
 = – c
C
21
 = – b
C
22
 = a
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
Also, A(adj A) = 
Hence, (adj A)A = |A|.I = A.(adj A)
1 C. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 
C
12
 = 
C
21
 = 
C
22
 = 
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
= 
= 
= 
Also, A(adj A) = 
= 
Hence, (adj A)A = |A|.I = A.(adj A)
1 D. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 1
C
12
 = 
C
21
 = 
C
22
 = 1
Since, adj A = 
(adj A) = 
= 
Page 4


7. Adjoint and Inverse of a Matrix
Exercise 7.1
1 A. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 4
C
12
 = – 2
C
21
 = – 5
C
22
 = – 3
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
Also, A(adj A) = 
A(adj A) = 
Hence, (adj A)A = |A|.I = A.(adj A)
1 B. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = d
C
12
 = – c
C
21
 = – b
C
22
 = a
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
Also, A(adj A) = 
Hence, (adj A)A = |A|.I = A.(adj A)
1 C. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 
C
12
 = 
C
21
 = 
C
22
 = 
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
= 
= 
= 
Also, A(adj A) = 
= 
Hence, (adj A)A = |A|.I = A.(adj A)
1 D. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 1
C
12
 = 
C
21
 = 
C
22
 = 1
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
= 
(adj A)A = 
And, |A|.I = 
= 
Also, A(adj A) = 
= 
= 
Hence, (adj A)A = |A|.I = A.(adj A)
2 A. Question
Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are:
C
11
 = – 3 C
21
 = 2 C
31
 = 2
C
12
 = 2 C
22
 = – 3 C
23
 = 2
C
13
 = 2 C
23
 = 2 C
33
 = – 3
adj A = 
= 
Page 5


7. Adjoint and Inverse of a Matrix
Exercise 7.1
1 A. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 4
C
12
 = – 2
C
21
 = – 5
C
22
 = – 3
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
Also, A(adj A) = 
A(adj A) = 
Hence, (adj A)A = |A|.I = A.(adj A)
1 B. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = d
C
12
 = – c
C
21
 = – b
C
22
 = a
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
Also, A(adj A) = 
Hence, (adj A)A = |A|.I = A.(adj A)
1 C. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 
C
12
 = 
C
21
 = 
C
22
 = 
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
(adj A)A = 
And, |A|.I = 
= 
= 
= 
Also, A(adj A) = 
= 
Hence, (adj A)A = |A|.I = A.(adj A)
1 D. Question
Find the adjoint of each of the following Matrices.
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are
C
11
 = 1
C
12
 = 
C
21
 = 
C
22
 = 1
Since, adj A = 
(adj A) = 
= 
Now, (adj A)A = 
= 
(adj A)A = 
And, |A|.I = 
= 
Also, A(adj A) = 
= 
= 
Hence, (adj A)A = |A|.I = A.(adj A)
2 A. Question
Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A are:
C
11
 = – 3 C
21
 = 2 C
31
 = 2
C
12
 = 2 C
22
 = – 3 C
23
 = 2
C
13
 = 2 C
23
 = 2 C
33
 = – 3
adj A = 
= 
Now, (adj A).A = 
= 
= 
Also, |A|.I =  = ( – 3 + 4 + 4)
= 
Then, A.(adj A) = 
= 
= 
Since, (adj A).A = |A|.I = A(adj A)
2 B. Question
Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)
Verify that (adj A) A=|A| I=A (adj A) for the above matrices.
Answer
A = 
Cofactors of A
C
11
 = 2 C
21
 = 3 C
31
 = – 13
C
12
 = – 3 C
22
 = 6 C
32
 = 9
C
13
 = 5 C
23
 = – 3 C
33
 = – 1
adj A = 
= 
Read More
204 videos|290 docs|139 tests

Top Courses for JEE

204 videos|290 docs|139 tests
Download as PDF
Explore Courses for JEE exam

Top Courses for JEE

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Important questions

,

mock tests for examination

,

shortcuts and tricks

,

video lectures

,

study material

,

Previous Year Questions with Solutions

,

practice quizzes

,

past year papers

,

Sample Paper

,

pdf

,

Free

,

Viva Questions

,

RD Sharma Class 12 Solutions - Adjoint and Inverse of a Matrix | Mathematics (Maths) Class 12 - JEE

,

ppt

,

MCQs

,

RD Sharma Class 12 Solutions - Adjoint and Inverse of a Matrix | Mathematics (Maths) Class 12 - JEE

,

Exam

,

Semester Notes

,

Summary

,

Objective type Questions

,

Extra Questions

,

RD Sharma Class 12 Solutions - Adjoint and Inverse of a Matrix | Mathematics (Maths) Class 12 - JEE

;