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

``` 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.
A =
Cofactors of A are
C
11
= 4
C
12
= – 2
C
21
= – 5
C
22
= – 3
=
And, |A|.I =
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.
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.
A =
Cofactors of A are
C
11
= 4
C
12
= – 2
C
21
= – 5
C
22
= – 3
=
And, |A|.I =
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.
A =
Cofactors of A are
C
11
= d
C
12
= – c
C
21
= – b
C
22
= a
=
And, |A|.I =
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.
A =
Cofactors of A are
C
11
=
C
12
=
C
21
=
C
22
=
=
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.
A =
Cofactors of A are
C
11
= 4
C
12
= – 2
C
21
= – 5
C
22
= – 3
=
And, |A|.I =
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.
A =
Cofactors of A are
C
11
= d
C
12
= – c
C
21
= – b
C
22
= a
=
And, |A|.I =
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.
A =
Cofactors of A are
C
11
=
C
12
=
C
21
=
C
22
=
=
And, |A|.I =
=
=
=
=
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.
A =
Cofactors of A are
C
11
= 1
C
12
=
C
21
=
C
22
= 1
=
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.
A =
Cofactors of A are
C
11
= 4
C
12
= – 2
C
21
= – 5
C
22
= – 3
=
And, |A|.I =
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.
A =
Cofactors of A are
C
11
= d
C
12
= – c
C
21
= – b
C
22
= a
=
And, |A|.I =
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.
A =
Cofactors of A are
C
11
=
C
12
=
C
21
=
C
22
=
=
And, |A|.I =
=
=
=
=
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.
A =
Cofactors of A are
C
11
= 1
C
12
=
C
21
=
C
22
= 1
=
=
And, |A|.I =
=
=
=
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.
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
=
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.
A =
Cofactors of A are
C
11
= 4
C
12
= – 2
C
21
= – 5
C
22
= – 3
=
And, |A|.I =
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.
A =
Cofactors of A are
C
11
= d
C
12
= – c
C
21
= – b
C
22
= a
=
And, |A|.I =
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.
A =
Cofactors of A are
C
11
=
C
12
=
C
21
=
C
22
=
=
And, |A|.I =
=
=
=
=
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.
A =
Cofactors of A are
C
11
= 1
C
12
=
C
21
=
C
22
= 1
=
=
And, |A|.I =
=
=
=
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.
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
=
=
=
Also, |A|.I =  = ( – 3 + 4 + 4)
=
=
=
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.
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
=
```

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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