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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 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 S consists of all points in R2 that are on the x-axis or the y-axis (or both). (S is called the union of the two axes.) Is S a subspace of R2? Why or why not?arrow_forward9. Show that P2 (polynomials of degree ≤ 2) is a subspace of P3 (polynomials of degree ≤ 3).arrow_forward
- Verify the Pythagorean Theorem for the orthogonal polynomials p(x) and q2(x) using the inner product from problem 2. Question 2 Inner product of p(x), q(x) is <P(x),Q(x)> = -3arrow_forwardMy question is verifying how V5 is a subspace of R^5arrow_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
- In each of the following determine the subspace of R2×2 consisting of all matrices that commute with the given matrix:arrow_forward1-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_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning