Do your eigenvectors obtained using Solve and those obtained using Eigenvectors agree? If not, is this a problem? Also if not, what (if any) is the relationship between them? 

What is the result of evaluating the following line of code (after completing exercises 4.1, 4.2 and 4.5)?

Simplify[M.evec1 == evals[[1]] evec1]&&Simplify[M.evec2 == evals[[2]] evec2]

In exercise 4.1 we ask that you characteristic equation and that requires the use of the identity matrix . How is a 2 x 2 identity matrix entered in Mathematica?

For this question select ALL answers that apply

The eigenvalues obtained using Solve and using Eigenvalues are the same

Exercise 3.7 asks you to summarise various key elements of ray tracing according to the things we have started to set up. 

In particular, please summarise here what the system matrix might look like for a ray moving a distance d1 encountering a thin lens and then moving a distance d2 and how we could combine (the matrices of) many lenses into a (system matrix for a) chain of lenses?

In exercise 3.3 you are asked to confirm that letting in the expression for Mthick reproduces the Mthin.  

Which of the following correctly checks for this (and returns True assuming Mthick and Mthin are correctly defined)?

Note there may be more than one correct answer, you only need to find one however.

In exercise 3.1 you are asked to form the matrix for a thick lens, and call it Mthick.

If you evaluate the following two lines:

MatrixForm[Mthick]

Which of the following is the output you obtain?

In exercise 2.1 you are asked to Solve for and to store the result into making sure to use replacement rules and pick out the solution of interest.  Which of the following is the resulting value of 

Read the background theory for this experiment and derive the equation for the Hall voltage of flowing water, assuming the equation derived in the previous question.

If you know the rate , in units of L/s, at which water flows out of a pipe with diameter , in units of m, how do you calculate the average velocity of the water, in units of m/s? (Show your work, provide relevant equations, explanations and diagrams.)