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Question
Find the values of a, b, c and d, if `|("a + 3b", 3"c" + "d"),(2"a" - "b" , "c" - 2"d")| = |(5 , 8),(3 , 5)|`
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Solution
`|("a + 3b", 3"c" + "d"),(2"a" - "b" , "c" - 2"d")| = |(5 , 8),(3 , 5)|`
a+ 3 b = 5 -(1)
2a - b = 3 -(2)
⇒ b = 2a - 3
putting this value of b in (1)
a + 6a - 9 = 5
⇒ 7a = 14
⇒ a = 2
from (i)
2+3 b = 5
⇒ 3 b = 3
⇒ b =1
3c + d = 8 ....(3)
c - 2d = 5 .....(4)
c = 5 + 2d
putting the value of c in (3)
15 + 6d + d = 8
⇒ 7 d = - 7
⇒ d = - 1
from(4)
c + 2 = 5
⇒ c = 3
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