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Question
Solve the following system of linear equations using matrix method:
3x + y + z = 1
2x + 2z = 0
5x + y + 2z = 2
Solution
3x + y + z = 1
2x + 2z = 0
5x + y + 2z = 2
A=`[(3,1,1),(2,0,2),(5,1,2)] ; "X" = [("x"),("y"),("z")] ; B = [(1),(0),(2)]`
A=`[(3,1,1),(2,0,2),(5,1,2)]`
|A| = 3(-2) -1 (-6) + 1(2) = -6 + 6 + 2 = 2 ≠ 0
`"adj A" =[(-2,6,2),(-1,1,2),(2,-4,-2)]^t = [(-2,-1,2),(6,1,-4),(2,2,-2)]`
`"A"^-1=1/2 [(-2,-1,2),(6,1,-4),(2,2,-2)]`
`"X"= "A"^-1 "B" = 1/2[(-2,-1,2),(6,1,-4),(2,2,-2)][(1),(0),(2)]`
`"X"= 1/2 [(2),(-2),(-2)] = [(1),(-1),(-1)]`
x = 1 , y = -1, z = -1.
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