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Question
If A = `[(9 , 1),(5 , 3)]` and B = `[(1 , 5),(7 , -11)]`, find matrix X such that 3A + 5B - 2X = 0.
Solution
Let X = `[(x , y),(z , u)]`
We have A = `[(9 , 1),(5 , 3)]` and B = `[(1 , 5),(7 , -11)]`
3A = `3[(9 , 1),(5 , 3)] = [(27 , 3),(15 , 9)]`
5B = `5[(1 , 5),(7 , -11)] = [(5 , 25),(35 , -55)]`
Now 3A + 5B - 2X = 0
⇒ `[(27 , 3),(15 , 9)] + [(5 , 25),(35 , -55)] + [(-2x , -2y),(-2z , -2u)] = [(0 , 0),(0 , 0)]`
⇒ `[(27 + 5 - 2x , 3 + 25 - 2y),(15 + 35 - 2z , 9 - 55 - 2u)] = [(0 , 0),(0 , 0)]`
⇒ `[(32 - 2x , 28 - 2y),(50 - 2z , -46 - 2u)] = [(0 , 0),(0 , 0)]`
⇒ 32 - 2x = 0 ⇒ 2x - 32 ⇒ x = 16
28 - 2y = 0 ⇒ 2y = 28 ⇒ y = 14
50 - 2z = 0 ⇒ 2z = 50 ⇒ z = 25
-46 - 2u = 0 ⇒ 2u = -46 ⇒ u = -23.
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