**Chapter 4 Determinants and Matrices Ex 4.5**

## Chapter 4 Determinants and Matrices Ex 4.5

**Question 1.**

Show that

i. A+B=B+A

ii. (A + B) + C = A + (B + C)

Solution:

Show that

i. A+B=B+A

ii. (A + B) + C = A + (B + C)

Solution:

From (i) and (ii), we get

A + B = B + A

**Question 2.Solution:**

**Question 3.If A = , B = then find the matrix C such that A + B + C is a zero matrix.Solution:**

A+ B + C is a zero matrix.

∴ A + B + C = O

C = -(A + B)

**Question 4.Solution:**

3A-4B + 5X = C

∴ 5X = C + 4B – 3A

**Question 5.**
By (i) x 3 – (ii) we get

**Question 6.**

By (i) – (ii) x 2, we get

**Question 7.Solution:**

**Question 8.**

**Show that A + B is singular. Is A – B singular? Justify your answer.Solution:**

**Question 9.Solution:**

∴ By equality of matrices, we get

∴ By equality of matrices, we get

2a + b = 2 ….(i)

3a – b = 3 ….(ii)

c + 2d = 4 ….(iii)

2c – d = -1 ….(iv)

Adding (i) and (ii), we get

5a = 5

∴ a = 1

Substituting a = 1 in (i), we get

2(1) + b = 2

∴ b = 0

By (iii) + (iv) x 2, we get

5c = 2

**Question 11.There are two book shops owned by Suresh and Ganesh. Their sales (in Rupees) for books in three subjects – Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B.i. Find the increase in sales in Rupees from July to August 2017.ii. If both book shops got 10% profit in the month of August 2017, find the profit for each bookseller in each subject in that month.Solution:**

i. Increase in sales in rupees from July to August 2017

For Suresh:

Increase in sales for Physics books

= 6650 – 5600= ₹ 1050

Increase in sales for Chemistry books

= 7055 – 6750 = ₹ 305

Increase in sales for Mathematics books

= 8905 – 8500 = ₹ 405

For Ganesh:

Increase in sales for Physics books

= 7000 – 6650 = ₹ 350

Increase in sales for Chemistry books

= 7500 – 7055 = ₹ 445

Increase in sales for Mathematics books

= 10200 – 8905 = ₹ 1295

[Note: Answers given in the textbook are 1760, 2090. However, as per our calculation they are 1050, 305, 405, 350, 445, 1295.]

ii. Both book shops got 10% profit in the month of August 2017.

For Suresh:

For Ganesh:

[Note: Answers given in the textbook for Suresh’s profit in Chemistry and Mathematics books are ? 675 and ?850 respectively. However, as per our calculation profit amounts are ₹ 705.50 and ₹ 890.50 respectively.]