Name two pairs of vectors that could span `RR^2`.  Show how the vector `(3, 2)` could be written as a linear combination of your spanning set.

Expert Answers
degeneratecircle eNotes educator| Certified Educator

One pair is the standard basis that consists of the vectors  `e_1=(1,0)` and `e_2=(0,1).` In this basis, `(3,2)=3e_1+2e_2.` 

Another pair that spans `RR^2` is `b_1=(3,2)` and `b_2=(1,1).` They do indeed span `RR^2` because neither is a multiple of the other. In this basis, `(3,2)=1b_1+0b_2.`