2 Marks Questions

Question 512 Marks

Find AB, if $A=\left[\begin{array}{ll} {6} & {9} \\ {2} & {3} \end{array}\right] \text { and } B=\left[\begin{array}{lll} {2} & {6} & {0} \\ {7} & {9} & {8} \end{array}\right]$

Answer

Matrix A has 2 columns which is equal to the number of rows of B. Hence AB is defined. Now
$A B=\left[\begin{array}{lll} {6(2)+9(7)} & {6(6)+9(9)} & {6(0)+9(8)} \\ {2(2)+3(7)} & {2(6)+3(9)} & {2(0)+3(8)} \end{array}\right]$
$=\left[\begin{array}{ccc} {12+63} & {36+81} & {0+72} \\ {4+21} & {12+27} & {0+24} \end{array}\right]$
$=\left[\begin{array}{ccc} {75} & {117} & {72} \\ {25} & {39} & {24} \end{array}\right]$

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Question 522 Marks

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 $\times$ 2 matrix. What does the entry in the third row and second column represent?

Answer

The information is represented in the form of a 3$\times$2 matrix as follows
$A=\left[\begin{array}{ll} {30} & {25} \\ {25} & {31} \\ {27} & {26} \end{array}\right]$
The entry in the third row and the second column represents the number of women workers in factory III.

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MATHS 2 Marks Questions