MHB 307w.WLCA.C10 computations are linear?

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the matrix at the bottom is from eMH but thot this was the way to do it... maybe not!
 
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Do you understand what this table tells you and what you are asked to do?

Let x be the number of kg of raisins used, y the number of kg of peanuts, z the number of kg of chocolate. Then one batch of "Bulk" mix requires 7x+ 6y+ 2z, one batch of "standard' mix requires 6x+ 4y+ 5z, and one batch of "Fancy" mix requires 2x+5y+ 8z.

The bottom row shows the cost of each kg of raisins, peanuts, and chocolate. x kg of peanuts costs 255x, y kg of peanuts cost 4.65y, and z kg of chocolate cost 4.80z so one batch of "Bulk" mix cost 7(4.65y)+ 6(4.65y)+ 2(4.80z)
 
ok I think in LA notation $ x_1, x_2, x_3$ is preferred for the matrix

why do you have y twice in 7(4.65y)+ 6(4.65y)+ 2(4.80z)
 
That was a typo, of course.

It should be 7(2.55x)+ 6(4.65y)+ 2(4.80z).
 
The world of 2\times 2 complex matrices is very colorful. They form a Banach-algebra, they act on spinors, they contain the quaternions, SU(2), su(2), SL(2,\mathbb C), sl(2,\mathbb C). Furthermore, with the determinant as Euclidean or pseudo-Euclidean norm, isu(2) is a 3-dimensional Euclidean space, \mathbb RI\oplus isu(2) is a Minkowski space with signature (1,3), i\mathbb RI\oplus su(2) is a Minkowski space with signature (3,1), SU(2) is the double cover of SO(3), sl(2,\mathbb C) is the...
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