Problem 4. Explain whether or not the following sets are subspaces of the given vector space +6] -b: a, beR of R'? (a) of R2? (c) {p(t) : p(1) = 1} of P2?
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Solved in 2 steps with 2 images
- Do questions 53 and 54 Show if it is a subspace using these 3 steps: 1. has to be equal to the 0 vector 2. has to be closed under addition 3. has to be closed under mulitplicationSuppose that S1 and S2 are subspaces of a vector space (V, F). Show that their intersection S1 ∩ S2 is also a subspace of (V, F). Is their union S1 ∪ S2 always a subspace?Based on other problems I believe the dimension is 3, but I'm not sure how to find a basis given this subspace.
- 10.Suppose that each of the vectors x(1), …, x(m) has n components, where n < m. Show that x(1), …, x(m) are linearly dependent. In each of Problems 11 and 12, determine whether the members of the given set of vectors are linearly independent for −∞ < t < ∞ . If they are linearly dependent, find the linear relation among them.Find a basis for the subspace of R3 spanned by S.S = {(4, 4, 8), (1, 1, 2), (1, 1, 1)}Find a basis for the subspace of R3 spanned by S. S = {(5, 9, 9), (1, 2, 2), (1, 1, 1)}
- if v is in R3, does the set of vectors x with v x x=0 is a subspace?Solve: (a) If a 7 x 9 matrix A has rank 5, what are the dimensions of the fourfundamental subspaces of A? (b) If a 3 x 4 matrix A has rank 3, what are the dimensions of R(A) and N(AT)?For which of the following pairs is the set Ω not a basis for the vector subspace U ≤ R2[x]?
- Problem 3: (2 marks) Let V = R be a vector space and let W be a subset of ', where W = {a,b,c):b = c² }. Determine, whether W is a subspace of vector space or not.the subset H={(x,y,z)∈ℝ³∣ 2x+3y-3z=4} it can be assured: * if u ∈H, v∈H , then u⊕v∈H* if u∈H, then c⊙u∈H, for all c∈R * H is a subspace of V=ℝ³ answer in each one if it is: False, true or cannot be established.Which of the following are vector subspaces of R3? all vectors of the form (a, b, c), where b = a + c? all vectors of the form (a, b, c), where b = a + c + 1? Note: In the image the problem is described more clearly, do not skip any step and solve the two parts a and b.