The enzyme alpha-amylase converts starch into small molecules such as glucose and maltose. Starch Small Molecules To characterize the kinetic behaviour of the enzyme, 5 different experiments were performed with different initial starch concentrations in an enzyme bioreactor. In each experiment, the corresponding reaction rate, V, was measured. The data is shared below. For a given input substrate concentration, you want to construct three models: a linear model (y^=a0+ a1x), a cubic model (y^=a0+a1x2+a2x3), and a model based on Michaelis-Menten equation for the prediction of reaction rate. a) Use the matrix equation derived in the class to predict the parameters for the linear model using Gaussian elimination. Calculate also R2 using the formula given in the class. b) Start from the objective function that defines the error. Derive the matrix equation for the cubic model. Show all the steps. Predict the parameter values using Gaussian elimination. Calculate R2 value, and compare the goodness of the model with the linear model you used in (a). c) Use the linearized Michaelis-Menten model (Lineweaver-Burk equation) derived in the model and Gauss-Jordan elimination to predict model parameters Km and Vmax. Calculate also R2 using the formula given in the class. Compare the model performance with the models in (a) and (b), discuss