SOLUTION: suppose A is a 3x3 matrix with elements a11 =1 a12=0 a13=2 a21=-1 a22=3 a23=4 a31=0 a32=1 a33=0 how would you use A^-1 to find the solutions of the linear system x+2z = 1 and

Algebra ->  Matrices-and-determiminant -> SOLUTION: suppose A is a 3x3 matrix with elements a11 =1 a12=0 a13=2 a21=-1 a22=3 a23=4 a31=0 a32=1 a33=0 how would you use A^-1 to find the solutions of the linear system x+2z = 1 and       Log On


   



Question 350586: suppose A is a 3x3 matrix with elements
a11 =1 a12=0 a13=2
a21=-1 a22=3 a23=4
a31=0 a32=1 a33=0
how would you use A^-1 to find the solutions of the linear system
x+2z = 1 and -x+3y+4z =2 and y=3
could you please show working.
i have used numbers with subscripts to depict the matrix entries because i dont know how to type the brackets

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
[A]=%28matrix%283%2C3%2C1%2C0%2C2%2C-1%2C3%2C4%2C0%2C1%2C0%29%29
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[A][x]=[b]
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where,
[x]=%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29
[b]=%28matrix%283%2C1%2C1%2C2%2C3%29%29
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[A][x]=[b]
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[A]inv[A][x]=[A]inv[b]
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Since [A]inv[A]=[I], then
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[x]=[A]inv[b]
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det[A]=-6
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[A]inv=%281%2F%28-6%29%29%2A%28matrix%283%2C3%2C-4%2C2%2C-6%2C0%2C0%2C-6%2C-1%2C-1%2C3%29%29
-6*([A]inv[b])=
-6*([A]inv[b])=%28matrix%283%2C1%2C-18%2C-18%2C6%29%29
Then,
[x]=%28matrix%283%2C1%2C3%2C3%2C-1%29%29