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Matrices

    • Question 1
    CBSEENMA12032843
    Wired Faculty App

    Consider the following information regarding the number of men and women workers in three factories I. II and III

     

    Men Workers

    Women Workers

    I

    30

    25

    II

    25

    31

    III

    27

    26

    Represent the above information in the form of a 3 x 2 matrix. What does the entry in the third row and second column represent ?

    Solution

    The given information is

    Factory

    Men Workers

    Women Worker:

    I

    , 30

    25

    II

    ' 25

    31

    III

    27

    26

    The information is represented in the form of a 3 X 2 matrix as follows :
    straight A equals open square brackets table row 30 25 row 25 31 row 27 26 end table close square brackets
    The entry in the third row and second column represents the number of women workers in factory III.

    Question 2
    CBSEENMA12032845
    Wired Faculty App

    In the matrix straight A equals open square brackets table row 2 5 19 cell negative 7 end cell row 35 cell negative 2 end cell cell 5 over 12 end cell 12 row cell square root of 5 end cell 1 cell negative 5 end cell 17 end table close square brackets. space Write

    (i) The order of the matrix
    (ii) The number of elements,
    (iii) Write the elements a13,a21 a33 a24’ a23

    Solution
    Here
    straight A equals left parenthesis straight a subscript straight i right parenthesis equals open square brackets table row 2 5 19 cell negative 7 end cell row 35 cell negative 2 end cell cell 5 over 12 end cell 12 row cell square root of 5 end cell 1 cell negative 5 end cell 17 end table close square brackets. space Write

    ( i) Now A has 3 rows and 4 columns and so A is of order 3 x 4.

    (ii) Number of elements = 3 x 4 = 12

    (iii) a13, =- 19., a21 =35, a33 = 5, J24 = 12, a23 equals 5 over 2

    Question 3
    CBSEENMA12032846
    Wired Faculty App

    If a matrix has 8 elements, what arc the possible orders it can have ?

     

    Solution

    We know' that if a matrix is of order m x n, it has mn elements. Therefore, for finding all possible orders of a matrix with 8 elements, we will find all ordered pairs of natural numbers, whose product is 8.

    ∴ all possible ordered pairs are (1.8), (8, I), (4, 2). (2, 4)
    ∴ possible orders are I x 8, 8 x 1, 2 x 4, 4 x 2.

    Question 4
    CBSEENMA12032848
    Wired Faculty App

    If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

    Solution

    We know that a matrix of order m x n has mn elements. Therefore, for finding all possible orders of a matrix with 24 elements, w e will find all ordered pairs with products of elements as 24.
    ∴ all possible ordered pairs are
    (1, 24), (24. 1), (2, 12), (12. 2). (3, 8), (8, 3), (4. 6), (6, 4)
    ∴ possible orders are
    1 x 24. 24 x 1, 2 x 12, 12 x 2, 3 x 8, 8 x 3, 4 x 6. 6 x 4
    If number of elements  =13, then possible orders are 1 x 13, 13 x l.

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