Let H be the set of all polynomials having a degree at most 4 and rational coefficients. Determine whether H is a vector space. If it is not a vector space, determine which of the following properties it fails to satisfy.A. Contains a zero vectorB. Closed under vector additionC. Closed under multiplication by scalar
H is not a vector space; not closed under multiplication by scalars
Let H be the set of all points in the xy-plane having at least one nonzero coordinate. H={[x/y]: x, y not both zero} Determine whether H is vector space. If it not a vector space, determine which of the following properties it fails to satisfy.A. Contains a zero vectorB. Closed under vector additionC. Closed under multiplication by scalar
H is not a vector space; fails to satisfy all three properties
Which is linearly independent?A: The set {p1, p2, p3} where p1(t)=1, p2(t)=t^2, p3(t)=2+3tB: The set {p1, p2, p3} where p1(t)=t, p2(t)=t^2, p3(t)=2+3t^2C: The set {p1, p2, p3} where p1(t)=1, p2(t)=t^2, p3(t)=2+3t+t^2
A and C
Given the set of vectors {{100], [010], [001], [011]} decide which of the following is true.
Set is linearly independent but does not span R3. Set is not a basis for R3.
Determine which of the following statements is false.
Any line in R3 is one-dimensional subspace of R3
Determine which of following statements is true.
If H is a subspace of a finite-dimensional vector space V, then dim H <= dim V