NCERT Solutions class 12 Maths Exercise 3.2

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NCERT Solutions class 12 Maths Exercise 3.2 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 Matrices as PDF.

NCERT Solutions class 12 Maths Exercise 3.2

NCERT Solutions class 12 Maths Matrices 

1. Let A =  B =  C = . Find each of the following:

(i) A + B

(ii) A – B

(iii) 3A – C

(iv) AB

(v) BA

Ans. (i) A + B =  =

(ii) A – B =  =

(iii) 3A – C =  =

(iv) AB =  =

(v) BA =  =


2. Compute the following:

(i)

(ii)  

(iii)

(iv)  

Ans. (i)   =

(ii)

=

(iii)   =

(iv)  =


3. Compute the indicated products:

(i)

(ii)  

(iii)

(iv)  

(v)

(vi)  

Ans. (i)  =

(ii)  =

(iii)  =

(iv)

=

  =

(v)

=

(vi)

=


4. If A =  B =  and C =  then compute (A + B) and (B – C). Also, verify that A + (B – C) = (A + B) – C.

Ans. A + B =  =  =

B – C =  =  =

Now, A + (B – C) = (A + B) – C

   =

   =

   =

 L.H.S. = R.H.S.  Proved.


5. If A =  and B =  then compute 3A – 5B.

Ans. 3A – 5B =

=

=


6. Simplify:  

Ans. Given:

=

=


7. Find X and Y, if:

(i) X + Y =  and X – Y =  

(ii) 2X + 3Y =  and 3X + 2Y =  

Ans. (i) Given: X + Y =   …..(i)

and X – Y =   …..(ii)

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

  2X =

  X =

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

  2Y =

  Y =

(ii) Given: 2X + 3Y =   …..(i)

 and 3X + 2Y =   …..(ii)

Multiplying eq. (i) by 2, 4X + 6Y =     ……….(iii)

Multiplying eq. (ii) by 3, 9X + 6Y =    ………(iv)

Eq. (iv) – Eq. (iii) = 5X =  =

 X =

Now, From eq. (i),  3Y =  2X =

  3Y =  =

  Y =


8. Fin X if Y =  and 2X + Y =  

Ans. 2X + Y =

 2X =  – Y

 2X =

 2X =

 X =  =


9. Find  and  if  

Ans. Given:

 

 

Equating corresponding entries, we have

 and

  and

  and

  and


10. Solve the equation for  and  if  

Ans. Given:

 

 

Equating corresponding entries, we have

         

And          

And    

And          

 , , ,


11. If  find the values of  and  

Ans. Given:

 

 

Equating corresponding entries, we have

 ……….(i) and   ……….(ii)

Adding eq. (i) and (ii), we have    

Putting  in eq. (ii),     


12. Given:  find the values of  and

Ans. Given:

 

Equating corresponding entries, we have

       

And

 

 

 

And      ……….(i)

And     

Putting  in eq. (i),  

    

  , , ,


13. If  show that  

Ans. Given:    ……….(i)

Changing  to  in eq. (i),

L.H.S. =

=

=

=

= R.H.S. [changing  to  in eq. (i)]


14. Show that:

(i)  

(ii)  

Ans. (i) L.H.S. =  =  =

R.H.S. =  =  =

  L.H.S.  R.H.S.

(ii) L.H.S. =

=

=

R.H.S. =

=

=

  L.H.S.  R.H.S.


15. Find A2 – 5A + 6I if A = .

Ans. A2 – 5A + 6I =

=

=  =

=


16. If A =  prove that A3 – 6A2 + 7A + 2I = 0.

Ans. L.H.S. = A3 – 6A2 + 7A + 2I

=

=

=

=  =

=  =

=  = 0 (Zero matrix)

= R.H.S.      Proved.


17. If A =  and I =  find  so that  

Ans. Given:  A =  and I =

     

 

 

Equating corresponding entries, we have

       

And       and        

 


NCERT Solutions class 12 Maths Exercise 3.2

18. If A =  and I is the identity matrix of order 2, show that 

Ans. L.H.S. = I + A =

Now, I – A =

R.H.S. =  =

=

=

=

=  =  =

  L.H.S. = R.H.S.         Proved.


19. A trust fund has ` 30,000 that must be invested in two different types of bond. The first bond pays 5% interest per year and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide ` 30,000 in two types of bonds, if the trust fund must obtain an annual interest of (a) ` 1800, (b) ` 2000.

Ans. Let the investment in first bond be ` , then the investment in the second bond = `

Interest paid by first bond = 5% =  per rupee and interest paid by second bond = 5% =  per rupee.

Matrix of investment is A =

Matrix of annual interest per rupee B =

Matrix of total annual interest is AB =  =

=  =

  Total annual interest = `

(a) According to question,

      

Therefore, Investment in first bond = ` 15,000

And Investment in second bond = ` (30000 – 15000) = ` 15,000

(b) According to question,

      

Therefore, Investment in first bond = ` 5,000

And Investment in second bond = ` (30000 – 15000) = ` 25,000


NCERT Solutions class 12 Maths Exercise 3.2

20. The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are ` 80, ` 60 and ` 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

Ans. Let the number of books as a 1 x 3 matrix B =

Let the selling prices of each book as a 3 x 1 matrix S =

  Total amount received by selling all books = BS =

=  =

Therefore, Total amount received by selling all the books = ` 20160


NCERT Solutions class 12 Maths Exercise 3.2

21. The restriction on  and  so that PY + WY will be define are:

(A)

(B)  is arbitrary,  

(C)  is arbitrary,

(D)  

Ans. Given:

Now,

On comparing,   and

Therefore, option (A) is correct.


NCERT Solutions class 12 Maths Exercise 3.2

22. If  then order of matrix 7X – 5Z is:

(A)

(B)

(C)

(D)  

Ans. Here  (given), the order of matrices X and Z are equal.

  7X – 5Z is well defined and the order of 7X – 5Z is same as the order of X and Z.

  The order of 7X – 5Z is either equal to  or

But it is given that

Therefore, the option (B) is correct.

NCERT Solutions class 12 Maths Exercise 3.2

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 13 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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