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.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter10: Classes And Data Abstraction

Section: Chapter Questions

Problem 19PE

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（Pyhton help）For Part a and b，PLS more details.

c) Ra = Pb is equivalent to the following equation that uses block form of matrices and vectors:
[R
-P][1] = 0
by using [R -P]¹ and tell us why it does not work. (Use np. linalg. pinv() to find the inverse of a non-
Use Python to solve for
square matrix)
Hint: Instantiate matrix R and P first, then combine them into one matrix M. Find inverse of the matrix M to check solutions for a, b.
Fill in the blank in the code cell below for part c, please use your own Python code to replace "..." parts. If you prefer, you can write your piece
of code from scratch instead (without filling in the blanks).
# Python code for part c goes here.
#Instantiate R as an numpy array from written solution.
R = np.array(.....)
#Instantiate P as an numpy array from written solution.
P = np.array(.....)
#Form a matrix as a matrix of R and -P which are developed above.
M = np.array(...)
#Inverse of the matrix developed to check for the solutions of a, b vectors.
N= np.linalg.pinv(...)

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.
b) Let a =
.b =
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.
c) Ra = Pb is equivalent to the following equation that uses block form of matrices and vectors:
8-
by using [R -P]¹ and tell us why it does not work. (Use np. linalg. pinv() to find the inverse of a non-
Use Python to solve for
square matrix)
[R -P
= 0

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