NCERT Solutions for Maths Class 12 Exercise 3.2

Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 3.2.

You can download the PDF of NCERT Books Maths Chapter 3 for your easy reference while studying NCERT Solutions for Maths Class 12 Exercise 3.2.
All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.
If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.
If you want to recall All Maths Formulas for Class 11, you can find it by clicking this link.

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 3.

Compute the indicated products.

Solution:

Maths Class 12 Ex 3.2 Question 4.

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

Solution:

Maths Class 12 Ex 3.2 Question 5.

,
then compute 3A – 5B.

Solution:

Maths Class 12 Ex 3.2 Question 6.

Simplify:

Solution:

Maths Class 12 Ex 3.2 Question 7.

Find X and Y, if

Solution:

Maths Class 12 Ex 3.2 Question 8.

Find X, if

Solution:
We have,

Maths Class 12 Ex 3.2 Question 9.

Find x and y, if

Solution:

We have,

Equating the elements, we have 2 + y = 5 and 2x + 2 = 8

This implies y = 3 and 2x = 6.
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,

Maths Class 12 Ex 3.2 Question 11.

find the values of x and y.

Solution:
We have,

Maths Class 12 Ex 3.2 Question 12.

Given

find the values of x, y, z and w.

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 13.

show that F(x).F(y) = F(x + y).

Solution:

Maths Class 12 Ex 3.2 Question 14.

Show that

Solution:

Hence, L.H.S. ≠ R.H.S.

Maths Class 12 Ex 3.2 Question 15.

Find A² – 5A + 6I, if A =

Solution:

We have A² = A.A

Maths Class 12 Ex 3.2 Question 16.

If A =

, prove that A³ – 6A² + 7A + 2I = 0

Solution:
We have A² = A.A

Maths Class 12 Ex 3.2 Question 17.

, 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.

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

Solution:
On the L.H.S:

On the R.H.S:

Maths Class 12 Ex 3.2 Question 19.

A trust fund has ₹ 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 ₹ 30,000 among the two types of bond if the trust fund must obtain an annual total interest of
(a) ₹ 1800 (b) ₹ 2000

Solution:
(a) Let ₹ x be invested in the first bond. Then, the sum of money invested in the second bond will be ₹ (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 ₹ 1800, the trust fund should invest ₹ 15,000 in the first bond and the remaining ₹ 15,000 in the second bond.

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

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

Thus, in order to obtain an annual total interest of ₹ 2000, the trust fund should invest ₹ 5000 in the first bond and the remaining ₹ 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 ₹ 80, ₹ 60 and ₹ 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 ₹ 80, ₹ 60 and ₹ 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 ₹ 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.

Related Links:

NCERT Solutions for Maths Class 12 Exercise 3.2

Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 3.2.