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Question
Find a matrix A such that 2A − 3B + 5C = 0, where B =`[(-2, 2, 0), (3, 1, 4)] and "C" = [(2, 0, -2),(7, 1, 6)]`.
Solution
Given: 2A − 3B + 5C = 0
⇒ `2"A" - 3 [(-2, 2, 0),(3,1,4)] +5 [(2,0,-2),(7,1,6)] = 0`
⇒ `2"A" - [(-6, 6, 0),(9,3,12)] + [(10,0,-10),(35,5,30)] = 0`
⇒ `2"A" + [(10+6,0 -6,-10 -0),(35 - 9 , 5 - 3 ,30 -12)] = 0`
⇒ `2"A" = -[(16 , -6, -10),(26, 2,18)]`
⇒ `"A" = [(-8,3,5),(-13,-1,-9)]`
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