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Question
Given that: A = `((1,-1,0),(2,3,4),(0,1,2))` and B = `((2,2,-4),(-4,2,-4),(2,-1,5))` , find AB. Using this result, solve the following system of equation: x – y = 3, 2x + 3y + 4z = 17 and y + 2z = 7.
Solution
AB = `[(1,-1,0),(2,3,4),(0,1,2)] [(2,2,-4),(-4,2,-4),(2,-1,5)]`
`=[(2+4+0, 2-2-0, -4+4+0),(4-12+8, 4+6-4, -8-12+20),(0-4+4, 0+2-2, 0-4+10)] = [(6,0,0),(0,6,0),(0,0,6)]`
AB = 6I3
A-1 AB = 6A-1 I
`1/6`B = A-1
Given system of equations are :
x - y = 3 , 2x + 3y + 4z = 17 and y + 2z = 7
Their matrix form is
AX = C
⇒ X = A-1 C
`= 1/6 [(6+34-28),(-12+34-28),(6-17+35)]`
`= 1/6 [(12),(-6),(24)] = [(2),(-1),(4)]`
Hence, x = 2 , y= -1 and z = 4
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