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Question
Find X and Y, if `X + Y = [(7,0),(2,5)] and X - Y = [(3,0),(0,3)]`
Solution
X + Y = `[(7, 0),(2, 5)]` .....(i)
X – Y = `[(3, 0),(0, 3)]` .....(ii)
Adding (i) and (ii) we get,
2x = `[(7, 0),(2, 5)] + [(3, 0),(0, 3)]`
= `[(7 + 3, 0 + 0),(2 + 0, 5 + 3)]`
= `[(10, 0),(2, 8)]`
∴ x = `(1)/(2)[(10, 0),(2, 8)]`
= `[(5, 0),(1, 4)]`
Subtracting (ii) from (i),
2y = `[(7, 0),(2, 5)] - [(3, 0),(0, 3)]`
⇒ 2y = `[(7 - 3, 0 - 0),(2 - 0, 5 - 3)]`
= `[(4, 0),(2, 2)]`
∴ y = `(1)/(2)[(4, 0),(2, 2)]`
= `[(2, 0),(1, 1)]`
Hence x = `[(5, 0),(1, 4)], "y" = [(2, 0),(1, 1)]`.
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