Chapter 3 Matrices Ex 3.2 Solutions
Question - 11 : - If
, find values of x and y.
Answer - 11 : - We have
Comparing thecorresponding elements of these two matrices, we get:
2x − y =10 and 3x + y = 5
Adding these twoequations, we have:
5x = 15
⇒ x = 3
Now, 3x + y =5
⇒ y = 5− 3x
⇒ y = 5− 9 = −4
∴x = 3 and y =−4Given
, find the values of x, y, z and w
Answer - 12 : - We have
Comparing thecorresponding elements of these two matrices, we get:
If
, show that 
.
Answer - 13 : - We have
Question - 14 : - Show that
Answer - 14 : -
(i) 
(ii) 
Question - 15 : - Find 
if 
Answer - 15 : -
We have A2 = A × A
Question - 16 : - If
, prove that 
Answer - 16 : - We have
Question - 17 : - If 
and
, find k sothat 
Answer - 17 : - We have
Comparing thecorresponding elements, we have:
Thus, the value of k is1.
If
and I is theidentity matrix of order 2, show that 
Answer - 18 : - We have
Question - 19 : - A trust fund has Rs30,000 that must be invested in two different types of bonds. The first bondpays 5% interest per year, and the second bond pays 7% interest per year.
Answer - 19 : -
Using matrix multiplication, determine how to divide Rs 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:
(a) Rs 1,800 (b) Rs 2,000
Solution
(a) Let Rs x be invested inthe first bond. Then, the sum of money invested in the second bond will be Rs
(30000 − x).
It is given that thefirst bond pays 5% interest per year and the second bond pays 7% interest peryear.
Therefore, in order toobtain an annual total interest of Rs 1800, we have:
Thus, in order toobtain an annual total interest of Rs 1800, the trust fund should invest Rs15000 in the first bond and the remaining Rs 15000 in the second bond.
(b) Let Rs x be invested inthe first bond. Then, the sum of money invested in the second bond will be Rs
(30000 − x).
Therefore, in order toobtain an annual total interest of Rs 2000, we have:
Thus, in order toobtain an annual total interest of Rs 2000, the trust fund should invest Rs5000 in the first bond and the remaining Rs 25000 in the second bond.
Question - 20 : - The bookshop of aparticular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozeneconomics books.
Answer - 20 : - 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
The bookshop has 10dozen chemistry books, 8 dozen physics books, and 10 dozen economics books.
The selling pricesof a chemistry book, a physics book, and an economics book are respectivelygiven as Rs 80, Rs 60, and Rs 40.
The total amount of moneythat will be received from the sale of all these books can be represented inthe form of a matrix as:Thus, the bookshopwill receive Rs 20160 from the sale of all these books.