Practice question · Multiple choice
An analyst tracks 12 macroeconomic series and finds they are all built from 3 underlying factors. What is that finding in vector-space language?
Hints
- Ask how many of the twelve you would need to reconstruct all twelve.
- Independence and dimension are two sides of the same count. Which is 3 here?
Show the answer
A. The 12 vectors span a 3-dimensional subspace
Why
Dimension counts genuinely independent directions rather than columns of data, so twelve series can carry three series' worth of information. Options 2 and 3 are self-contradictory, you cannot have twelve independent vectors in a three-dimensional space, and this is exactly what factor models exploit.
Practise Vector Spaces
The app has 6 more questions on this lesson, and keeps your place in the course. Business I is free to start.
More questions on Vector Spaces
- Order the reasoning to find the dimension of the space spanned by a set of vectors.
- Sort each investment-menu situation by its linear-algebra diagnosis.
- Match each concept to its definition.
- Why must every basis of ℝ³ have exactly three vectors, never two, never four?
- Which statements about span and independence are true?
- (2,2) and (3,3) together span only the line y = x, while (1,0) and (0,1) span the whole plane. What does that…
- Four vectors in ℝ³ can be linearly independent.