1. ( 30 Points) For a matrix a=8264.22.4288.72.9 (1) Use Matlab to calculate the determinant of the matrix (2) Justify if the matrix has the inverse matrix and use Matlab to calculate the inverse Matrix (3) Use Matlab to calculate the eignvalues and eignvectors of the Matrix 2. (35 Points) Enzymatic reactions are modeled using a model v=kmS3/(K+S3) where v is the initial rate of the reaction (M/s),S is the substrate concentration (M),km and K are parameters. The following data can be fit with the model Use linear fitting to estimate parameters, km and K and evaluate the curve fitting. 3. (35 Points) Calculate the volume of 10.0kgCO2 at 25C and 4 bar (gas phase). Use the van der Waals equation. It is known vdW parameters: a=1.474bar(kmolm2)2,b=0.0395kmolm3 This question is required to use Matlab nonlinear solver to get the solution