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Solutions ⇒ Class 12th ⇒ Mathematics-I ⇒ 3. Matrices

# Solutions 3. Matrices - Exercise 3.2 | Class 12 Mathematics-I - Toppers Study

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## Solutions 3. Matrices - Exercise 3.2 | Class 12 Mathematics-I - Toppers Study

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Chapter 3 Mathematics-I class 12

### Exercise 3.2 class 12 Mathematics-I Chapter 3. Matrices

• Solutions 3. Matrices - Exercise 3.2 | Class 12 Mathematics-I - Toppers Study
• Class 12 Ncert Solutions
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• Chapter 3. Matrices Exercise 3.2 Class 12

## Solutions 3. Matrices - Exercise 3.2 | Class 12 Mathematics-I - Toppers Study

Exercise 3.2

Ques.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 =  =

Ques.2. Compute the following:

(i)

(ii)

(iii)

(iv)

Ans. (i)   =

(ii)

(iii)   =

(iv)  =

Ques.3. Compute the indicated products:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Ans. (i)  =

(ii)  =

(iii)  =

(iv)

=

(v)

(vi)

Ques.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.

hance Proved.

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

Ans. 3A – 5B =

Ques.6. Simplify:

Ans. Given:

### Ques.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)

subtracting Eq. (iii) from Eq. (iv)

5X =

X =

Now, From eq. (i),  3Y =  2X =

3Y =  =

Y =

Ans. 2X + Y =

2X =  – Y

2X =

2X =

X =  =

### Ques.9. Find  and  if

Ans. Given:

Equating corresponding entries, we have

and

and

and

and

### Ques.10. Solve the equation for  and  if

Ans. Given:

Equating corresponding entries, we have

And

And

And

### Ques.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),

### Ques.12. Given:  find the values of  and

Ans. Given:

Equating corresponding entries, we have

And

And      ……….(i)

And

Putting  in eq. (i),

### Ques.13. If  show that

Ans. Given:    ……….(i)

Changing  to  in eq. (i),

L.H.S. =

= R.H.S. [changing  to  in eq. (i)]

### Ques.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.

### Ques.15. Find A2 – 5A + 6I if A = .

Ans. A2 – 5A + 6I =

=

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

Ans. L.H.S. = A3 – 6A2 + 7A + 2I

=

=

= 0 (Zero matrix)

= R.H.S.

hance Proved.

### Ques.17. If A =  and I =  find  so that

Ans. Given:  A =  and I =

Equating corresponding entries, we have

And       and

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

Ans. L.H.S. = I + A =

and, I – A =

R.H.S. =  =

=  =

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

hance Proved.

### Ques.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 = ,

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,

hance, Investment in first bond = ` 15,000

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

(b) According to question,

hance, Investment in first bond = ` 5,000

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

### Ques.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 =

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

### Ques.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

hance, option (A) is correct.

Ques.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

hance, the option (B) is correct.

##### Other Pages of this Chapter: 3. Matrices

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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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