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The following are some recommended conceptual self-assessment questions for the lesson called Linearizing the parametric functional model. They’re intended for you to work through to test your own understanding of the key concepts we covered there.

Question 1

a) What is \mathbf{A}\boldsymbol{\delta} - \mathbf{e} + \mathbf{w} =\mathbf{0}?

b) What is each term called and what does each term mean?

c) What is the equation for each term?

d) What dimensions does each term have?

e) Which term is most dependent on Taylor’s Theorem?

f) Why is the equation in a) so important?

Question 2

In Example 1 of the video accompanying this topic, we treated point B as having unknown coordinates and point A as having known coordinates, i.e. where the number of unknowns u = 2.

Derive the equations for each term in the \mathbf{A} matrix for the more general case where the coordinates of point A are also unknown, i.e. where the number of unknowns u = 4. You don’t need to compute the numerical values here. Just take the partial derivatives required and provide the equations you would use for computing the numerical values for each spot in the 1 x 4 matrix.

Question 3

If you have the following functional model:

l_{true} = f(x) = 3x + 6x^2 + 9x^3 in mm

a) Is it linear or non-linear in x? Explain.

b) What is the corresponding equation for each row of the design matrix \mathbf{A}?

If you’re one of my students, then you’re expected to answer these on your own and submit them according to the directions provided in class, i.e. you don’t  need to submit them through this website. Don’t forget that our TA and I are both here to help you in the associated lab (and/or tutorial) sessions.

I want you to put your answers to these conceptual questions into a single document. I don’t mind if you hand write it or type it out – do what works best for you.

But I want you to use the same document for all of the self-assessment questions you do before the due date, i.e. you will be asked to hand them all in together. This means you should keep things well organized with clear headings so you (and your TA) can figure out which solutions refer to which questions. Good self-assessment documents use headings and some even provide the links, e.g. the URL for this page. This helps you keep track and go back and forth quickly between the problems and solutions.

Also, keep in mind that you will be asked to submit them through D2L, so you’ll have to scan any handwritten documents.

You can click through to other self-assessments or lessons (if any) using the button below, and return here whenever you wish.