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 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 A**^{2} – 5A + 6I if A = .

^{2}– 5A + 6I if A = .

**Ans. **A^{2} – 5A + 6I =

=

= =

=

**16. If A = prove that A**^{3} – 6A^{2} + 7A + 2I = 0.

^{3}– 6A

^{2}+ 7A + 2I = 0.

**Ans. **L.H.S. = A^{3} – 6A^{2} + 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

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