Question 1101074: If parcel A and B together weigh 24 kgs, but parcel B and C together weighs only 21 kgs. When parcel A and C are paired, the combined weight is 27kgs. If the weight of parcel A is represented by a, the weight of parcel B is represented by b and the weight of parcel C is represented by c a. Derive a system of three equations in a, b and c. b. Using the inverse method derive the combined weight of parcel A, B and C.
Found 2 solutions by ankor@dixie-net.com, richwmiller:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! If the weight of parcel A is represented by a, the weight of parcel B is represented by b and the weight of parcel C is represented by c a.
Derive a system of three equations in a, b and c. b.
Using the inverse method derive the combined weight of parcel A, B and C.
:
If parcel A and B together weigh 24 kgs,
a + b = 24
but parcel B and C together weighs only 21 kgs.
b + c = 21
When parcel A and C are paired, the combined weight is 27kgs.
a + c = 27
:
write the system like this
a + b + 0 = 24
0 + b + c = 21
a + 0 + c = 27
------------------Add
2a + 2b + 2c = 72
simplify divide by 2
a + b + c = 36 kg is the combined weight of the 3 parcels
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:
Not sure if this is the inverse method, but this sure is the simplest.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! original
1 1 0 24
0 1 1 21
1 0 1 27
determinant =2
inverse matrix fractional form
1/2 -1/2 1/2
1/2 1/2 -1/2
-1/2 1/2 1/2
24 21 27
solutions and sum
15 + 9 + 12 =36
The process is much too long to present here.
I can only assume that such a problem was given to practice the inverse matrix method so that you could check your result easily with ankor's method..
There are several inverse matrix methods including using gauss jordan, using the identity matrix and using determinants, cofactors and and adjoint.
I used determinant, cofactor and and adjoint.
Ankor's method didn't need to find a,b and c individually.
Yesterday, Ikleyn used a similar method as Ankor to solve the same problem stating it is the most obvious and simplest choice to solve this problem. It is but I suppose that the teacher is introducing inverse matrix method and started with an easy system of equations
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