Class 12 Maths

# Matrices

## NCERT Solution

### Exercise 2 Part 10

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 the second bond pays 7& interest per year. Using matrix multiplication, determine how to divide Rs. 30,000 among the types of bonds. If the trust fund must obtain an annual total interest of:

(a) Rs. 1800 (b) Rs. 2000

Solution: Let RS x is invested @5% interest per year.

Therefore, investment @7% interest peryear = RS (30000 – x)

Therefore, matrix of the investments = [x(30000) – x]

Matrix of interest Therefore, interest per year =  Thus, investment @5% per year = Rs 15000

And the investment @ 7% per year = 30000 – 15000 = 15000 Thus, investment @ 5% per year = Rs 5000

And the investment @7% = 30000 – 5000 = Rs. 25000

Question 20: The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices 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: Here, matrix of number of books = [10 dozen, 8dozen, 10 dozen]
=[120 96 120]

Matrix of cost= Therefore, total amount Assume X, Y, Z, W and P are matrices of order 2 × n, 3 × k, 2 × p, n × 3 and p × k, respectively. Choose the correct answer in Exercises 21 and 22.

Question 21: The restriction 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

Answer: (A) k = 3, p = n

Explanation: In this order of p = p x k

Order of w = n x 3

And order of y = 3 x k

Thus, order of py = p x k, when k = 3

And the order of wy = p x k, when p = n

Thus, option (A) is correct

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

Explanation:

In this order of X = 2 x n

And order of Z = 2 x p

Therefore, n = p

Therefore order of 7X – 5Z = 2 x n

Thus, option (B) is correct.

Exercise 3.1

Exercise 3.2