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# NCERT Solutions class 12 Maths Exercise 4.5

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## NCERT Solutions class 12 Maths Determinants

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

1.

Ans. Here A =

A11 = Cofactor of

A12 = Cofactor of

A21 = Cofactor of

A22 = Cofactor of

2.

Ans. Here A =

=

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

3.

Ans. Let A =

=  =   …..(i)

=  =     …..(ii)

And  =

Again      …..(iii)

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

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.

5.

Ans. Let A =

=  0

Matrix A is non-singular and hence  exist.

6.

Ans. Let A =

=

Matrix A is non-singular and hence  exist.

7.

Ans. Let A =

=

exists.

A11 = ,  A12 = ,

A13 = ,   A21 = ,

A22 = ,   A23 = ,

A31 = ,   A32 = ,

A33 =

8.

Ans. Let A =

=

exists.

A11 = , A12 = ,

A13 = , A21 = ,

A22 = , A23 = ,

A31 = ,   A32 = ,

A33 =

9.

Ans. Let A =

=

exists.

A11 = , A12 = ,

A13 = , A21 = ,

A22 = , A23 = ,

A31 = ,  A32 = ,

A33 =

10.

Ans. Let A =

=

exists.

A11 = ,  A12 = ,

A13 = , A21 = ,

A22 = , A23 = ,

A31 = , A32 = ,

A33 =

11.

Ans. Let A =

=

exists.

A11 = ,

A12 = , A13 = ,

A21 = ,   A22 = ,

A23 = ,  A31 = ,

A32 = , A33 =

### 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.

### 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 .

=

=  =

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

Ans. Given: A =

We have ……….(i)

Here  satisfies  also, therefore

Putting  in eq. (i),

Here also  satisfies  , therefore

Therefore,  and

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

Ans. Given: A =

=

Now

=

=

L.H.S. =

=

=

=

=  =  = R.H.S.

Now,   to find , multiplying  by

=

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

Ans. Given: A =

=

Now

=

=

L.H.S. =

=

=

=

=  =  = R.H.S.

Now,   to find , multiplying  by

=

### 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

Therefore, option (B) is correct.

### 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

Therefore, option (B) is correct.

## NCERT Solutions class 12 Maths Exercise 4.5

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 20 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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### 2 thoughts on “NCERT Solutions class 12 Maths Exercise 4.5”

1. Very nice solution it is helpful for the students

2. Thank u so much 4 help it is useful and easy