Exercise 5.1 Exercise 5.2 Exercise 5.3

**EXERCISE 5.1**

Question 1

**If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?**

**Sol:**

Order of matrix = number of rows number of column

**OR**

Total number of elements = number of rows number of column

Thus, to find all possible order of a matrix having 8 elements we have to find all possible ordered pairs whose product is 8.

Possible order pairs are

(1 8) ; (8 1) ; (2 4) ; (4 2) ;

**AND**

The possible orders of a matrix with 5 total elements are

(1 5) ; (5 1)

Question 2

**If ** and then find

**(i) ****(ii) **

**Sol :**

(i)

where,

and

= 4 + (-3)

= 1

(ii)

where,

= (2)(2) + (4)(4)

= 4 + 16

= 20

Question 3

**Let A be a matrix of order 3 4.If denotes the first row of A and denotes second column, then determine the orders of matrices and **

Question 4

**Construct a 2 3 matrix whose elements are given by:**

**(i) **

**(ii) **

**(iii) **

**(iv) **

Question 5

**Construct a 2 2 matrix whose elements are given by:**

**(i) **

****

**(ii) **

****

**(iii)**

****

**(iv)**

****

**(v)**

****

**(vi)**

****

Question 6

**Construct a 3 4 matrix A=[] whose elements are given by:**

**(i)**

**(ii)**

**(iii)**

**(iv)**

**(v)**

Question 7

**Construct a matrix 4 3 matrix whose elements are **

**(i) **

**(ii)**

**(iii)**

Question 8

**Find x,y,a and b if **

Sol :

Question 9

**Find x,y,a and b if **

**(i) **

Question 10

**Find the value of a,b,c and d from the following equations:**

Sol :

Question 11

**For what values of x and y are the following matrices equal ?**

Sol :

Question 12

**Find x,y and z so that A=B,where**

Sol :

Question 13

**If **

Sol :

Question 14

**If **

Sol :

Question 15

**Find the values of x and y if **

Sol :

Question 16

**If**

**Obtain the value of a,b,c,x,y and z.**

Sol:

Question 17

**Give an example of (i)a row matrix which is also a column matrix, (ii)a diagonal matrix which is not scalar, (iii)a triangular matrix **

Question 18

**The sale figure of two car dealers during January 2007 showed that dealer A sold 5 deluxe, 3 premium and 4 standard cars,while dealer B sold 7 deluxe, 2 premium and 3 standard cars.Total sales over the 2 month periods of January-February revealed that dealer A sold 8 deluxe 7 premium and 6 standard cars.In the same 2 month period, dealer B sold 10 deluxe, 5 premium and 7 standard cars.Write 2 3 matrices summarizing sales data for January and 2 month periods for each dealer.**