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- Is S = {(x1, x2)^T ∈ R^2| x1 > x2} a subspace of R^2? Justify your answer.arrow_forward10.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_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_forward
- For any planes P1 and P2 (possibly equal) in R3, each of which passes through theorigin, the following set is a subspace of R3: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_forwardMy question is verifying how V5 is a subspace of R^5arrow_forward
- 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.arrow_forward9. Show that P2 (polynomials of degree ≤ 2) is a subspace of P3 (polynomials of degree ≤ 3).arrow_forwardIn each of the following determine the subspace of R2×2 consisting of all matrices that commute with the given matrix:arrow_forward
- 1-Suppose that S1and S2are nonzero subspaces, with S1 contained inside S2, and suppose that dim(S2)=3(a) What are the possible dimensions of S1? (b) If S1≠S2then what are the possible dimensions of S1? 2-Find the dimensions of the following linear spaces. (a) ℝ4×2(b) P3(c) The space of all diagonal 6×6 3-Find a basis {p(x),q(x)} for the vector space {f(x)∈P2[x]∣f′(4)=f(1)}where P2[x] is the vector space of polynomials in xx with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5+3x^2p(x) , q(x)= 4-A square matrix is half-magic if the sum of the numbers in each row and column is the same. Find a basis BB for the vector space of 2×2 half-magic squares. B=arrow_forwardShow that W = {(x1, x2): x1 ≥ 0 and x2 ≥ 0}, with the standard operations, is not a subspace of R2.arrow_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