Question

Three shopkeepers A, B and C go to a store to buy stationery. A purchase 12 dozen note-books, 5 dozen pens and 6 dozen pencils. B purchase 10 dozen note-books, 6 dozen pens and 7 dozen pencils. C purchase 11 dozen note-books, 13 dozen pens and 8 dozen pencils. A note book costs 40 paise, a pen costs Rs. 1-25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual’s bill.

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Solution

straight A space purchases space 144 space note minus books comma space 60 space pens comma space 72 space pencils straight B space purchases space 120 space note minus books comma space 72 space pens comma space 84 space pencils. straight C space purchases space 132 space note minus books comma space 156 space pens comma space 96 space pencils. Let space space be space the space matrix space of space purchases. straight D equals space open square brackets table row 140 60 72 row 120 72 84 row 132 156 96 end table close square brackets Let space straight E space be space the space price space matrix. therefore space straight E equals space open square brackets table row cell 0.40 end cell row cell 1.25 end cell row cell 0.35 end cell end table close square brackets therefore DE equals space space open square brackets table row 140 60 72 row 120 72 84 row 132 156 96 end table close square brackets space space open square brackets table row cell 0.40 end cell row cell 1.25 end cell row cell 0.35 end cell end table close square brackets space space space space space space space space space space space equals open square brackets table row cell 57.60 plus 75.00 plus 25.20 end cell row cell 48.00 plus 90.00 plus 29.40 end cell row cell 52.80 plus 195.00 plus 33.60 end cell end table close square brackets space equals space open square brackets table row cell 157.40 end cell row cell 157.80 end cell row cell 281.40 end cell end table close square brackets bill space of space straight A comma space straight B comma space straight C space are space Rs. space 157.80 comma space Rs. space 167.40 space and space Rs. space 281.40 space respectively.

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Matrices

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