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How could I arrange a matrix of 4 alloys with Cu,Zn and Pb composition to determine the % comp. of new alloy?
Cu 54 53 54 51
Zn 31 32 29 30
Pb 3 2 4 3
Get a new alloy with 53.2% Cu 30.2% Zn and 3.2% Pb using the four Alloys mention above. Total amount mixed 600Kg.
I have tried all kinds of arrangements in the matrix to obtain x,y.z and w, but the results do not have any logic. Deteminants is cool and fun but this one got me. Anybody please help.
2 réponses
- Fly On The WallLv 7il y a 1 décennieRéponse favorite
First define a matrix of four alloy compositions be a 3 x 4 matrix we'll call "A". Let your amounts of the four different alloys be a 4-vector we'll call "X". (the four elements of X are what you called w, x, y, and z). Let 600 Kg be a simple scalar value we'll call "S". And finally define a second 4-vector "B" that is the fractional content of each metal in the new alloy. The elements of "B" are therefore 0.532, 0.302, and 0.032. When you multiply the 3 x 4 matrix times your 4-vector X (which is a 4 x 1 column matrix), then you should get a 3-vector (S times B).
Thus your equation is AX = SB, and you are meant to solve for X. You need to take the inverse of A so that you can write:
X = S(A-inverse)B
Thus you do have to invert a matrix but you shouldn't need to calculate any determinants.
- ?Lv 4il y a 5 ans
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