** ** **NCERT Solutions for Maths Class 12 Exercise 3.2**

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Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

**NCERT Solutions for Maths Class 12 Exercise 3.2** helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

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**NCERT Solutions for Maths Class 12 Exercise 3.2** are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

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**NCERT Solutions for Maths Class 12 Exercise 3.1**

**NCERT Solutions for Maths Class 12 Exercise 3.3**

**NCERT Solutions for Maths Class 12 Exercise 3.4**

**NCERT Solutions for Maths Class 12 Exercise 3.2**

** **

**Maths Class 12 Ex
3.2 Question 1.**

**Let**

**Find each of the following:**

**(i) A + B (ii)
A – B (iii) 3A –
C**

**(iv) AB (v)
BA**

**Solution:**

**Maths
Class 12 Ex 3.2 Question 2.**

**Compute the following:**

**Solution:**

**Maths Class 12 Ex
3.2 Question 4.**

**If**,

**then compute (A + B) and (B – C). Also verify that A + (B – C) = (A + B) –
C.**

**Solution:**

**Solution:**

We have,

**Maths Class 12 Ex
3.2 Question 9.**

**Solution:**

We have,

Hence, x = 3 and y = 3.

**Maths
Class 12 Ex 3.2 Question 10.**

**Solve the equation for x, y, z and t, if**

**Solution:**

We have,

**Solution:**

We have,

⇒ 3x = x + 4 ⇒ x = 2

And 3y = 6 + x + y ⇒ y = 4

Also, 3w = 2w + 3 ⇒ w = 3

Again, 3z = – 1 + z + w

⇒ 2z = – 1 + 3

⇒ 2z = 2

⇒ z = 1

Hence, x = 2, y = 4, z = 1, w = 3.

**Maths Class 12 Ex
3.2 Question 15.**

**Find A² – 5A + 6I, if A =**

**Solution:**

*A*² =

*A.A*

**Maths Class 12 Ex
3.2 Question 16.**

**If A =**

**, prove that A³ – 6A² + 7A + 2I = 0**

**Solution:**

We have

*A*² =

*A.A*

**Maths Class 12 Ex
3.2 Question 17.**

**If**

**, find k so that A² = kA – 2I**

**Solution:**

We are given that,

We have to find the value of k.

Now, A² = kA – 2I

**Maths Class 12 Ex
3.2 Question 18.**

**If**

**and I is the identity matrix of order 2, show that**

**Solution:**

On the L.H.S:

**Maths Class 12 Ex
3.2 Question 19.**

**A trust fund has Rs 30,000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bond if the trust fund must obtain an annual total interest of**

**(a) Rs 1800 (b) Rs 2000**

**Solution:**

**(a)** Let Rs *x *be
invested in the first bond. Then, the sum of money invested in the second bond
will be Rs (30,000 − *x*).

It is given that the first bond pays 5% interest per year and the
second bond pays 7% interest per year.

Therefore, in order to obtain an annual total interest of Rs 1800,
we have:

Thus, in order to obtain an annual total interest of Rs 1800, the
trust fund should invest Rs 15,000 in the first bond and the remaining Rs 15,000
in the second bond.

**(b) **Let Rs *x *be invested in the first bond. Then, the sum of
money invested in the second bond will be Rs (30,000 − *x*).

Therefore, in order to obtain an annual total interest of Rs 2000,
we have:

Thus, in order to obtain an annual total interest of Rs 2000, the trust fund should invest Rs 5000 in the first bond and the remaining Rs 25,000 in the second bond.

**Maths Class 12 Ex
3.2 Question 20.**

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

**Solution:**

The bookshop has 10 dozen chemistry books, 8 dozen physics books,
and 10 dozen economics books.

The selling prices of a chemistry book, a physics book, and an
economics book are given as Rs 80, Rs 60 and Rs 40, respectively.

The total amount of money that will be received from the sale of
all these books can be represented in the form of a matrix as:

Thus, the bookshop will receive Rs 20160
from the sale of all these books.

**Assuming X, Y, Z,
W and P are the matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k,
respectively. Choose the correct answer in questions 21 and 22.**

**Maths Class 12 Ex
3.2 Question 21.**

**The restrictions on n, k and p so that PY + WY will be defined are**

**(A) k = 3, p = n**

**(B) k is arbitrary, p = 2**

**(C) p is arbitrary, k = 3**

**(D) k = 2, p = 3**

**Solution:**

Given: X_{2 x n,} Y_{3 x k}, Z_{2 x p,} W_{n
x 3, }P_{p x k}

Now PY + WY = P_{p x k} × Y_{3 + k} + W_{n x 3} ×
Y_{3 x k}

Clearly, k = 3 and p = n

Hence, option (A) is correct.

**Maths Class 12 Ex
3.2 Question 22.**

**If n = p, then the order of the matrix 7X – 5Z is:**

**(A) p × 2**

**(B) 2 × n**

**(C) n × 3**

**(D) p × n**

**Solution:**

7X – 5Z = 7X

_{2 x n}– 5Z

_{2 x p}

We can add two matrices if their order is the same, i.e., n = P.

Therefore, the order of 7X – 5Z is 2 × n.

Hence, option (B) is correct.