Quiz 2
UQ MATH7502
Mathematics for Data Science 2 (2020)

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The quiz will be made available online here on Sep 14, 4:55pm (Brisbane time). It is to be submitted no later than 6:30pm.

The quiz is closed material meaning that you cannot use any written material, internet material, communication with others, software (Julia), or anything else during the quiz. You can eat, drink, standup, sit down, walk around, pet your cat, and go the restroom during the quiz. But any other interaction with the outside world dealing with the quiz is prohibited. You may only use a double sided A4 formula sheet that you will prepare prior to the quiz and a simple (scientific) calculator.

The duration of the quiz is 70 minutes + an additional 20 minutes for uploading the quiz. Your upload should include: (1) A scan of the quiz according to the instructions here. (2) The scan file should also include both sides of your double sided A4 sheet - place these after the quiz solution. (3) A short voice recording specifying that you adhered to the instructions and kept it honest. The recording can share any other experience you had during the quiz. Again follow the instructions here.

The material for Quiz 2 is the following:
  1. All of the material of Quiz 1 and...
  2. Vector spaces
  3. The range of a matrix, the null space of the matrix
  4. Relationships between the fundamental subspaces of a matrix
  5. Linear independence
  6. Orthogonal vectors and properties of matrices with orthonormal columns
  7. The Gram-Schmidt procedure
  8. QR factorizations
  9. Projections onto a line and a subspace
  10. Solving least squares using the Moore–Penrose inverse
Here are some suggested practice problems:
[LALFD]:
From Problem Set I.3: Q3, p20. Q7, p20. Q10, p20.
From Problem Set I.5: Q1, p35. Q5, p35.

[VMLS]:
Q5.3, p103. Q5.6, p103. Q5.7, p104. Q11.12, p219. Q11.18, p120.

[ILA]:
From Problem Set 3.1: Q4, p131. Q25, p134. Q29, p134.
From Problem Set 3.2: Q22, p144. Q24, p144. Q25, p144. Q48, p147. Q49, p147.
From Problem Set 3.4: Q2, p175. Q8, p175. Q15, p176.
From Problem Set 3.5: Q13, p191. Q23, p192.
From Problem Set 4.2: Q1, p214. Q13, p216.

Here is the Quiz. Here is the solution.