Need help solving these problems please

For each problem on this page, perform the matrix computation and then select all correct answers that apply from the following list for each problem. You must show your hand-written work to get credit. Here are the multiple choice options for each of these four problems:

A. diagonal matrix B. triangular matrix

C.integrating factor

D.Jeffersonian matrix

E.identity matrix

F.invertible matrix

G.non-invertible (a.k.a. singular) matrix

H.symmetric matrix

I.technically it is not a matrix

1.(5 points) Compute and classify.

?3

2.(5 points) Compute and classify?4.

341

3.(5 points) Compute and classify.

1For the vaccine modeling fans

4.(5 points) In class, we studied one model for perfect vaccine efficacy and three models for imperfect vaccine efficacy (the all-or-nothing model, the leaky model, and the three-factor model). Based on the article, rank the models from (1) most appropriate to (4) least appropriate for modeling of the Pfizer/Moderna vaccines. Explain your reasoning in 2-3 sentences.

5.(10 points) Our models in class did not differentiate between those with one dose and those with two doses. Write down the flow diagram for a SIR model of disease transmission with two additional stages of vaccination calledV₁andV₂. Assume that (a) susceptible people receive the first dose of vaccine at a per-capita rate?, (b) people with one dose receive the second dose at a per-capita rate?/2, (c) both stagesV₁andV₂follow a leaky model with vaccine efficaciesV E₁andV E₂, respectively. Label your diagram with typical SIR constants, and additional vaccine-related values as appropriate.

6.(10 points) Write a system of differential equations corresponding to this system.

7.(5 points) Find the equilibrium or equilibria in this system. Explain it/them in words.

For each problem on this page, perform the matrix computation and then select all correct answers that apply from the following list for each problem. You must show your hand-written work to get credit. Here are the multiple choice options for each of these four problems: A. diagonal matrix B. triangular matrix C. integrating factor D. Jeffersonian matrix E. identity matrix F. invertible matrix G. non-invertible (a.k.a. singular) matrix H. symmetric matrix I. technically it is not a matrix 1. (5 points) Compute and classify M = ( ) ( 3) 2. (5 points) Compute and classify M = 3. (5 points) Compute and classify M = (6) (e f)