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Question
Find the 2 x 2 matrix X which satisfies the equation.
`[(3, 7),(2, 4)][(0 , 2),(5 , 3)] + 2"X" = [(1 , -5),(-4 , 6)]`
Solution
`[(3, 7),(2, 4)][(0 , 2),(5 , 3)] + 2"X" = [(1 , -5),(-4 , 6)]`
⇒ `[(0 + 356 + 21),(0 + 204 + 12)] + 2X = [(1 , -5),(-4 , 6)]`
⇒ `[(35 , 27),(20 , 16)] + 2X = [(1 , -5),(-4 , 6)]`
⇒ 2X = `[(1 , -5),(-4 , 6)]`
`-[(35 , 27),(20 , 16)]`
⇒ 2X = `[(-34 , -32),(-24, -10)]`
⇒ X = `[((-34)/(2) (-32)/(2)), ((-24)/(2) (-10)/(2))]`
⇒ X = `[(-17 , -16),(-12 , -5)]`
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