7. Span, Linear Independence, Basis, and Dimension

Constructing Bases And Coordinate Representations — Quiz

Test your understanding of constructing bases and coordinate representations with 5 practice questions.

Practice Questions

Question 1

Which statement best describes a basis of a vector space?

Question 2

In a $2$-dimensional space, let $B={(1,0),(0,1)}$. What are the coordinates of $v=(4,-3)$ with respect to $B$?

Question 3

Let $B={(1,2),(3,1)}$. Which coordinate vector represents $v=(-1,3)$ with respect to $B$?

Question 4

How many vectors are in any basis of a $5$-dimensional vector space?

Question 5

What is the coordinate vector of the zero vector with respect to any basis of a $3$-dimensional vector space?