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Solutions ⇒ Class 12th ⇒ Mathematics-I ⇒ 4. Determinants

# Solutions 4. Determinants - Exercise 4.5 | Class 12 Mathematics-I - Toppers Study

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## Solutions 4. Determinants - Exercise 4.5 | Class 12 Mathematics-I - Toppers Study

CBSE board students who preparing for class 12 ncert solutions maths and Mathematics-I solved exercise chapter 4. Determinants available and this helps in upcoming exams 2023-2024.

### You can Find Mathematics-I solution Class 12 Chapter 4. Determinants

• All Chapter review quick revision notes for chapter 4. Determinants Class 12
• NCERT Solutions And Textual questions Answers Class 12 Mathematics-I
• Extra NCERT Book questions Answers Class 12 Mathematics-I
• Importatnt key points with additional Assignment and questions bank solved.

Chapter 4 Mathematics-I class 12

### Exercise 4.5 class 12 Mathematics-I Chapter 4. Determinants

• Solutions 4. Determinants - Exercise 4.5 | Class 12 Mathematics-I - Toppers Study
• Class 12 Ncert Solutions
• Solution Chapter 4. Determinants Class 12
• Solutions Class 12
• Chapter 4. Determinants Exercise 4.5 Class 12

## Solutions 4. Determinants - Exercise 4.5 | Class 12 Mathematics-I - Toppers Study

Exercise 4.5

Find adjoint of each of the matrices in Exercise 1 and 2.

Ques.1.

Ans. Here A =

A11 = Cofactor of

A12 = Cofactor of

A21 = Cofactor of

A22 = Cofactor of

Ques.2.

Ans. Here A =

=

Verify A (adj. A) =  in Exercise 3 and 4.

Ques.3.

AnsLet A =

=   …..(i)

=     …..(ii)

And  =

Again      …..(iii)

From eq. (i), (ii) and (iii)

Ques.4.

Ans. Let A =

=

=

……….(i)

……….(ii)

And

Also  =     ……….(iii)

From eq. (i), (ii) and (iii)  A. (adj. A) = (adj. A). A =

### Find the inverse of the matrix (if it exists) given in Exercise 5 to 11.

Ques.5.

Ans. Let A =

=  0

Matrix A is non-singular and hence  exist.

Ques.6.

Ans. Let A =

=

Matrix A is non-singular and hence  exist.

Ques.7.

Ans. Let A =

=

exists.

A11 = ,  A12 = ,

A13 = ,   A21 = ,

A22 = ,   A23 = ,

A31 = ,   A32 = ,

A33 =

Ques.8.

Ans. Let A =

=

exists.

A11 = , A12 = ,

A13 = , A21 = ,

A22 = , A23 = ,

A31 = ,   A32 = ,

A33 =

Ques.9.

Ans. Let A =

=

exists.

A11 = , A12 = ,

A13 = , A21 = ,

A22 = , A23 = ,

A31 = ,  A32 = ,

A33 =

Ques.10.

Ans. Let A =

exists.

A11 = ,  A12 = ,

A13 = , A21 = ,

A22 = , A23 = ,

A31 = , A32 = ,

A33 =

Ques.11.

Ans. Let A =

exists.

A11 = ,

A12 = , A13 = ,

A21 = ,   A22 = ,

A23 = ,  A31 = ,

A32 = , A33 =

### Ques.12. Let A =  and B =  verify that

Ans. Given: Matrix A =

= 15 – 14 = 1  0

=

Matrix B =

= 54 – 56 =   0

Now AB =  =  =

=

Now L.H.S. =     ……….(i)

R.H.S. =

……….(ii)

From eq. (i) and (ii), we get

L.H.S. = R.H.S.

### Ques.13. If A = , show that A2 – 5A + 7I = 0. Hence find

Ans. Given: A =

L.H.S. =

= R.H.S.

……(i)

To find: , multiplying eq. (i) by .

=

Ques.14. For the matrix A =  find numbers  and  such that

Ans. Given: A =

We have  ……….(i)

Here  satisfies  also, so

Putting  in eq. (i),

Here also  satisfies  , so

hance,  and

### Ques.15. For the matrix A = , show that  Hence find

Ans. Given: A =

=

Now

L.H.S. =

=  = R.H.S.

Now,   to find , multiplying  by

=

### Ques.16. If A = , verify that  and hence find

Ans. Given: A =

=

Now

L.H.S. =

=  = R.H.S.

Now,   to find , multiplying  by

=

### Ques.17. Let A be a non-singular matrix of order 3 x 3. Then  is equal to:

(A)

(B)

(C)

(D)

Ans. If A is a non-singular matrix of order  then

Putting

hance, option (B) is correct.

### Ques.18. If A is an invertible matrix of order 2, then det  is equal to:

(A) det A

(B)

(C) 1

(D) 0

Ans. Since

hance, option (B) is correct.

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## Study Materials List:

##### Solutions ⇒ Class 12th ⇒ Mathematics-I
1. Relations and Functions
2. Inverse Trigonometric Functions
3. Matrices
4. Determinants
5. Continuity And Differentiability
6. Application of Derivatives

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