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Question
If A = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)]` and B = `[(x),(y),(z)]`, find the matrix B'(AB)
Solution
AB = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)] [(x),(z),(y)]`
= `[(3y + 3z),(-3x + 4z),(-3x + 4y)]`
B'(AB) = `[(x),(y),(z)] [(3y + 3z),(-3x - 4z),(-3x + 4y)]`
= `[(x, y, z)] [(3y + 3z),(-3x - 4z),(-3x + 4y)]`
= [3xy + 3xz − 3xy − 4yz − 3xz + 4yz]
= [0]
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AB = [ ]
|AB| = `square`
M11 = –2 ∴ A11 = (–1)1+1 . (–2) = –2
M12 = –3 A12 = (–1)1+2 . (–3) = 3
M21 = 4 A21 = (–1)2+1 . (4) = –4
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adj (A) = [ ]
A–1 = `1/|A| . adj(A)`
A–1 = `square`
