NCERT Solutions class 12 Maths Exercise 4.5

CBSE Sample Papers 2018-19

myCBSEguide App


Install myCBSEguide mobile app for FREE sample papers, Test Papers, Revision Notes, Previous year question papers, NCERT solutions and MCQ tests. Refer myCBSEguide App to your friends and Earn upto Rs.500/-.
myCBSEguide AppmyCBSEguide app install

NCERT Solutions class 12 Maths Exercise 4.5 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

Download NCERT solutions for Determinants  as PDF

NCERT Solutions class 12 Maths Exercise 4.5

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

 adj. A =  =


2.  

Ans. Here A =

 

      =

 adj. A =


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

3.  

Ans. Let A =

adj. A =

 A.(adj. A) =

=  =   …..(i)

Again  (adj. A). A =

=  =     …..(ii)

And  =

Again      …..(iii)

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


4.  

Ans. Let A =

  

    =

 

 

  

 adj. A =

 A. (adj. A) =

 =

= ……….(i)

Again  (adj. A). A =

=

=   ……….(ii)

And

=

Also  =     ……….(iii)

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


NCERT Solutions class 12 Maths Exercise 4.5

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.

Now adj. A =  And


6.  

Ans. Let A =

  =

 Matrix A is non-singular and hence  exist.

Now adj. A =  And


7.  

Ans. Let A =

  =

  exists.

A11 = ,  A12 = ,

A13 = ,   A21 = ,

A22 = ,   A23 = ,

A31 = ,   A32 = ,

A33 =

 adj. A =

 


8.  

Ans. Let A =

   =

  exists.

A11 = , A12 = ,

A13 = , A21 = ,

A22 = , A23 = ,

A31 = ,   A32 = ,

A33 =

 adj. A =

 


9.  

Ans. Let A =

  =

  exists.

A11 = , A12 = ,

A13 = , A21 = ,

A22 = , A23 = ,

A31 = ,  A32 = ,

A33 =

 adj. A =

 


10.  

Ans. Let A =

  =

  exists.

A11 = ,  A12 = ,

A13 = , A21 = ,

A22 = , A23 = ,

A31 = , A32 = ,

A33 =

 adj. A =

 


11.  

Ans. Let A =

 

=

  exists.

A11 = ,

A12 = , A13 = ,

A21 = ,   A22 = ,

A23 = ,  A31 = ,

A32 = , A33 =

 adj. A =

 


NCERT Solutions class 12 Maths Exercise 4.5

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.

 


NCERT Solutions class 12 Maths Exercise 4.5

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 .

 

 

 

=

=  =


NCERT Solutions class 12 Maths Exercise 4.5

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


NCERT Solutions class 12 Maths Exercise 4.5

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

Ans. Given: A =

 

  =

Now

=

=

L.H.S. =

=

=

=

=  =  = R.H.S.

Now,   to find , multiplying  by

 

 

 

 

 

  =

 


NCERT Solutions class 12 Maths Exercise 4.5

16. If A = , verify that  and hence find

Ans. Given: A =

 

  =

Now

=

=

L.H.S. =

=

=

=

=  =  = R.H.S.

Now,   to find , multiplying  by

 

 

 

 

 

  =

 


NCERT Solutions class 12 Maths Exercise 4.5

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.


NCERT Solutions class 12 Maths Exercise 4.5

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

CBSE App for Class 12

To download NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through the best app for CBSE students and myCBSEguide website.


Deal of the Day
Latest Sample Papers 149/-
Test Paper & Worksheets 299/-
Click Here & Tap Shop

1 thought on “NCERT Solutions class 12 Maths Exercise 4.5”

Leave a Comment