Linear Combinations of Vectors

If a set of vectors V is closed under addition and scalar multiplication, what can you conclude about V?

• V is a vector space

• V is a subspace of a larger vector space.

• V is not a set of vectors

The zero vector is always a member of any subspace

• True

• False

• I dont no

If u is in the null space of matrix A, what happens when you multiply u by a scalar c?

• cu becomes the zero vector

• cu remains in the null space of A.

• cu is no longer a solution to

• The answer depends on the specific matrix A.

• A

• B

• C

• D

Given u = <3, 7> and v =<-5, 4>, find 2v - 3u

• <21, 2>

• <-19, -13>

• <-15, 3>

• 23

If y = <1, 1> and v = <6, 8>, what is 6y + 2v?

• <38, 50>

• <17, 30>

• <18, 22>

• 16, 20>

If g = <-1, 1>, y = <1, 1>, z = <-3, -3>, and v = <6, 8>, what is 4g + y + z - 5v?

• <24, 42>

• <-36, -38>

• <36, 38>

• <-30, -32>

f = 〈 - 2, - 12〉 v = 〈6, - 7〉 Find: 2f − 3v

• 〈16, - 3〉

• 〈 - 22, - 3〉

• 〈 - 5, 4〉

• 〈14, - 3〉

Given
v = 〈3,-5〉 and 
w = 〈-2,3〉, what is 2v + 3w?

• 〈6,-10〉

• 〈1,-2〉

• 〈0,-1〉

• none of these

Write your answer as a linear combination (no spaces)