A shopkeeper has 3 varieties of pens 'A','B' and 'C'. Meena purchased 1 pen of each variety for a total of Rs.21.Jeevan purchased 4 pens of 'A' variety, 3 pens of 'B' variety and 2 pens"c" variety for Rs.60. while Shika purchased 6 pens of 'A' variety, 2 pens of 'B' variety and 3 pens of 'C' variety for Rs.70. Using matrix method, find cost of each variety of pen.(HOW TO SOLVE THIS QUESTION)

Asked by reach2abhijeetsingh | 6th Aug, 2016, 05:08: PM

Expert Answer:

begin mathsize 16px style From space the space given space information space we space can space form space straight a space matrix space as space follows

open square brackets table row 1 1 1 row 4 3 2 row 6 2 3 end table close square brackets open square brackets table row straight A row straight B row straight C end table close square brackets equals open square brackets table row 21 row 60 row 70 end table close square brackets

Applying space straight R subscript 2 rightwards arrow straight R subscript 2 minus 4 straight R subscript 1 comma space straight R subscript 3 rightwards arrow straight R subscript 3 minus 6 straight R subscript 1
open square brackets table row 1 1 1 row 0 cell negative 1 end cell cell negative 2 end cell row 0 cell negative 4 end cell cell negative 3 end cell end table close square brackets open square brackets table row straight A row straight B row straight C end table close square brackets equals open square brackets table row 21 row cell negative 24 end cell row cell negative 56 end cell end table close square brackets

Applying space space straight R subscript 3 rightwards arrow straight R subscript 3 plus left parenthesis negative 4 right parenthesis straight R subscript 2
open square brackets table row 1 1 1 row 0 cell negative 1 end cell cell negative 2 end cell row 0 0 5 end table close square brackets open square brackets table row straight A row straight B row straight C end table close square brackets equals open square brackets table row 21 row cell negative 24 end cell row 40 end table close square brackets

From space above space we space get space three space equations comma

straight A space plus straight B plus straight C space equals 21............ left parenthesis straight i right parenthesis
negative straight B minus 2 straight C space equals negative 24............ left parenthesis ii right parenthesis
5 straight C space equals space 40
straight C space equals space 8............. left parenthesis iii right parenthesis

Substituting space straight C space equals space 8 space in space left parenthesis ii right parenthesis comma space we space get comma
minus straight B minus 2 left parenthesis 8 right parenthesis space equals space minus 24
straight B space equals space 8

Substituting space straight c space equals space 8 space and space straight B space equals space 16 space in space left parenthesis straight i right parenthesis comma space we space get comma
straight A space plus 8 plus 8 space equals 21
straight A space equals space 5


Cost space of space apostrophe straight A apostrophe space variety space pen space is space Rs. space 5 comma space apostrophe straight B apostrophe space variety space pen space is space Rs. space 8 space space and space space apostrophe straight C apostrophe space variety space pen space is space Rs. space 8.




end style

Answered by Vijaykumar Wani | 8th Aug, 2016, 11:13: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.