Let us consider the problem of balancing the photosynthesis equation (the reason humans exist), where plants take in CO₂ and produces 0₂. sunlight a₁CO₂ + a₂H₂O ⇒ b₁C6H12O6 + b₂O₂, a₁, a2, b₁, b2 ‡ 0 In other words, we are looking to find the values of a₁, a2, b₁, b2 so that this chemical equation is "balanced". A "balanced" equation is an sunlight equation that makes sure that the number of C, O, H atoms on both sides of is equal. a) Write a system of linear equations that establish a relation between the unknown variables a₁, a2, b₁,b₂. NOTE : Show it mathematically along with words, equations and explanations. You can use latex or upload a written answer in the text cell below. Write your answer for part a here. · - [C] = [] ,b= b) Let a = Write the above linear equations in a) in matrix vector format, expressing the matrix R (reactant matrix) as an independent matrix multiplying the vector a on the left hand side, and matrix P (product matrix) as an independent matrix multiplying the vector b on the right hand side, thus forming a matrix vector equation in the form Ra = Pb. NOTE: Please have some word explanation for identifying the matrices according to the chemical equation, show it on latex or upload a written answer in the text cell before Write your answer for part b here.

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