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CBSE Class 12-science Answered

An amont of 600 crores is spent by the Government in 3 Schemes (A,B,C). Now twice the amount spent on Scheme C together with the amount spent on Scheme A is Rs. 700 crores. Three times the amount spent on Scheme A  together with the amount spent on Scheme B and Scheme C is Rs. 1200 crores.Find the amount spent on each scheme using matrices.
Asked by Jayesh Pradhyumna | 28 Jan, 2015, 04:59: PM
answered-by-expert Expert Answer
L e t space t h e space s c h e m e s space b e space A comma B space a n d space C. C plus A plus B equals 600..... left parenthesis i right parenthesis 2 C plus A equals 700....... left parenthesis i i right parenthesis 3 A plus B plus C equals 1200..... left parenthesis i i i right parenthesis T h e space e q u a t i o n s space c a n space b e space w r i t t e n space a s C plus A plus B equals 600..... left parenthesis i right parenthesis C plus 3 A plus B equals 1200..... left parenthesis i i i right parenthesis 2 C plus A equals 700....... left parenthesis i i right parenthesis I n space M a t r i x space f o r m comma open square brackets table row 1 1 1 row 1 3 1 row 2 1 0 end table close square brackets open square brackets table row C row A row B end table close square brackets equals open square brackets table row 600 row 1200 row 700 end table close square brackets P X equals Q S i m p l i f y i n g space P comma open square brackets table row 1 1 1 row 1 3 1 row 2 1 0 end table close square brackets equals open square brackets table row 1 1 1 row 1 5 1 row 2 0 0 end table close square brackets 2 C subscript 2 minus C subscript 1 rightwards arrow C subscript 2 equals open square brackets table row 1 1 4 row 1 5 0 row 2 0 0 end table close square brackets 5 C subscript 3 minus C subscript 2 rightwards arrow C subscript 3 N o w comma open square brackets table row 1 1 1 row 1 3 1 row 2 1 0 end table close square brackets open square brackets table row C row A row B end table close square brackets equals open square brackets table row 600 row 1200 row 700 end table close square brackets rightwards double arrow open square brackets table row 1 1 4 row 1 5 0 row 2 0 0 end table close square brackets open square brackets table row C row A row B end table close square brackets equals open square brackets table row 600 row 1200 row 700 end table close square brackets S o l v i n g space t h e space m a t r i x comma space w e space g e t space A equals 950 over 4 equals 237.5 space c r o r e s B equals 350 space c r o r e s C equals 50 over 4 equals 12.5 space c r o r e s
Answered by Prasenjit Paul | 29 Jan, 2015, 11:33: AM

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