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You go to the shops on Monday and buy 1 apple, 1 banana, and 1 carrot; the whole transaction totals €15. On Tuesday you buy 3 apples, 2 bananas, 1 carrot, all for €28. Then on Wednesday 2 apples, 1 banana, 2 carrots, for €23.
Construct a matrix and vector for this linear algebra system.
Matrix is A = [ [ A₁₁ , A₁₂ , A₁₃]
[ A₂₁ , A₂₂ , A₂₃]
[ A₃₁ , A₃₂ , A₃₃] ]
Vector S = [sMon , sTue , sWed]
(i) consider A as fruits
A₁₁ = 1
A₁₂ = 1
A₁₃ = 1
A₂₁ = 3
A₂₂ = 2
A₂₃ = 1
A₃₁ = 2
A₃₂ = 1
A₃₃ = 2
(ii) Consider s as days
sMon = 15
sTue = 28
sWed = 23
Hence the matrix and vector is: A = [ [ A₁₁ , A₁₂ , A₁₃]
[ A₂₁ , A₂₂ , A₂₃]
[ A₃₁ , A₃₂ , A₃₃] ]
Vector S = [sMon , sTue , sWed]
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