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Question
A = `[(3, 0),(4, 5)]`, B = `[(6, 3),(8, 5)]`, C = `[(3, 6),(1, 1)]` find the matrix D, such that CD – AB = 0
Solution
Given A = `[(3, 0),(4, 5)]`, B = `[(6, 3),(8, 5)]`, C = `[(3, 6),(1, 1)]`
Let D be `[("a", "b"),("c","d")]`
Given CD – AB = 0
AB = CD
`[(3, 0),(4, 5)] [(6, 3),(8, 5)] = [(3, 6),(1, 1)] [("a", "b"),("c", "d")]`
`[(18 + 0, 9 + 0),(24 + 40, 12 + 25)] = [(3"a" + 6"c", 3"b" + 6"d"),("a" + "c", "b" + "d")]`
`[(18, 9),(64, 37)] = [(3"a" + 6"c", 3"b" + 6"d"),("a" + "c", "b" + "d")]`
3a + 6c = 18
(÷ 3) ⇒ a + 2c = 6 ....(1)
a + c = 64 ....(2)
(–) (–) (–)
(1) – (2) ⇒ c = – 58
Substitute the value of c = – 58 in (1)
a – 116 = 6
a = 6 + 116
= 122
3b + 6d = 9
(÷ 3) ⇒ b + 2d = 3 ....(3)
b + d = 37 ....(4)
(–) (–) (–)
(3) – (4) ⇒ d = – 34
Substitute the value of d = – 34 in (4)
b – 34 = 37
b = 37 + 34
= 71
Matrix D = `[(122, 71),(- 58, - 34)]`
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