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