SOLUTION: Hi, Nick here, was hoping someone might be able to give me a hand with writing the following system of equations in the matrix form and solve using inverse matrix. x + 2y = 6 ,

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Question 196182: Hi, Nick here, was hoping someone might be able to give me a hand with writing the following system of equations in the matrix form and solve using inverse matrix.
x + 2y = 6 ,
3x + 4y = 2
I also have to solve the system using the elimination procedure and compare the two answers.
Any help would be great. -Nick
Answer by anantha(86) (Show Source):
You can put this solution on YOUR website!
sol:
matrix equations obtained from the equations a1x+b1y+c1=0
a2x+b2y+c2=0 is
[a1 b1][x]=[-c1]
[a2 b2][y]=[-c2]
write the given equations in the mmatrix notation
x+2y=6
3x+4y=2
[1 2][x]=[6]
[3 4][y]=[2]
here A=[1 2] X= [x] B=[6]
[3 4] [y] [2]

the matrix equation of the form
AX=B
x=A^-1B
A^-1=1/ad-bc [d -b]
[-c a]
=1/4-6 [4 -2]
[-3 1]
=1/-2 [4 -2]
[-3 1]
=[4/-2 -2/-2]
[-3/-2 1/-2]
X=A^-1*B
X=[4/-2 -2/-2][6]
[-3/-2 1/-2][2]
=[4/-2*6 + -2/-2*2]
[-3/-2*6+ 1/-2*2]
[-12+2]
[9-1]
X= [-10]
[8]
[x]=[-10]
[y]=[8]