Theory test: Vectors and matrices

6 questions. Pass with 5 correct.

1. 01 What is the dot product of $(1,2,3)$ and $(4,-5,6)$?

   1232−12$(4,-10,18)$
2. 02 Two non-zero vectors point in exactly opposite directions. Their cosine similarity is:

   01−1It depends on their lengths
3. 03 $A$ has shape $(3,4)$ and $B$ has shape $(4,2)$. What is the shape of $AB$?

   $(4,4)$$(3,2)$$(2,3)$It is undefined
4. 04 X has shape (100, 5). Which line raises a broadcasting error?

   X - X.mean(axis=0)X - X.mean(axis=1)X - X.mean(axis=1, keepdims=True)X * 2
5. 05 A $2\times 2$ matrix has determinant 0. What does it do to the plane?

   Rotates it without stretchingLeaves every point where it isSquashes it onto a line or a point, so it cannot be undoneDoubles every area
6. 06 Why do ML libraries compute $X\mathbf{w}$ instead of looping over rows?

   It gives a more accurate answerIt scores every example in one vectorised operation that runs in compiled, parallel codeLoops are not allowed in PythonIt uses less memory than storing $X$