7. Span, Linear Independence, Basis, and Dimension

Coordinate Systems — Quiz

Test your understanding of coordinate systems with 5 practice questions.

Practice Questions

Question 1

In the standard coordinate system for $\mathbb{R}^2$, what are the coordinates of the vector $\left(3,-5\right)$?

Question 2

With basis $B=\{\left(2,0\right),\left(0,5\right)\}$, what are the coordinates of $\left(6,10\right)$ with respect to $B$?

Question 3

With basis $B=\{\left(1,1\right),\left(1,-1\right)\}$, what are the coordinates of $\left(3,1\right)$ with respect to $B$?

Question 4

How many numbers are in the coordinate vector of any vector in $\mathbb{R}^3$ with respect to a basis for $\mathbb{R}^3$?

Question 5

Which statement best describes a coordinate system in linear algebra?