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- 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.arrow_forwarddeal with the problem of solving Ax = b when det A = 0.22.Suppose that, for a given matrix A, there is a nonzero vector x such that Ax = 0. Show that there is also a nonzero vector y such that A*y = 0.arrow_forwardProblem 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.arrow_forward
- Is S = {(x1, x2)^T ∈ R^2| x1 > x2} a subspace of R^2? Justify your answer.arrow_forwardFor question 6: Determine if the vector u is in the column space of matrix A and whether it is in the null space of Aarrow_forwardSuppose 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?arrow_forward
- 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.arrow_forwardFor Problem #12, how do I prove that the set is a basis for V? I think that infinity is the basis, but I'm not sure. This is a Linear Algebra type of question. Here is a picture.arrow_forwardthe 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.arrow_forward
- Determine the dimensions of the following subspaces of R4 All vectors of the form (a, b, c, d), where d = a + b y c = a – b. All vectors of the form (a, b, c, d), where a = b = c = d. Note: In the image the problem is described more clearly, do not skip any step and solve the two parts a and b.arrow_forwardThis question is regarding vectors and matrices, what do I match these 4 parts with when the 5 choices to match with are: It equals 1 It is meaningless It equals 0 It equals 4 It equals the zero vectorarrow_forwardFrom my linear algebra course practice problems: "Is the subset of polynomials for which p(-1) = p(0) = p(5) a subspace of the vector space of all polynomials? Justify your reasoning." I'm aware of the 3 criteria needed to be met for a subset to be considered a subspace, but I just have no idea how to approach determining whether the zero vector is in the subset, and whether addition and multiplication are closed to the set.arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning