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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.

Insert math as
$${}$$