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Question
If A = `|(3,-2),(-1 , 4)|` , B = `|(2"a"),(1)|` , C = `|(-4),(5)|` , D = `|(2),("b")|` and AB + 2C = 4D then find the values of a and b.
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Solution
A = `|(3,-2),(-1 , 4)|_(2 xx 2)` , B = `|(2"a"),(1)|_(2 xx 1)`
C = `|(-4),(5)|_(2 xx 1)` , D = `|(2),("b")|_(2 xx 1)`
AB = `|(3,-2),(-1 , 4)| |(2"a"),(1)|`
`= |(6"a" - 2),(-2"a" + 4)|_(2 xx 1)`
2C = `|(-8),(10)|`
AB + 2C = `|(6"a" - 2),(-2"a" + 4)| |(-8),(10)|`
`= |(6"a" - 10),(-2"a" + 14)|_(2 xx 1)`
4D = `|(8),(4"b")|`
Given, AB + 2C = 4D
`|(6"a" - 10),(-2"a" + 14)| = |(8) , (4"b")|`
6a - 10 = 8
⇒ 6a=18
⇒ a = 3
- 2a + 14 = 4b
⇒ -2(3 )+ 14 =4 b
⇒ 8 = 4 b
⇒ 2 = b
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