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- Given = -8 6 6 -1-8 and 2 -16 2 , find the closest point to in the subspace W spanned by 0 5arrow_forwardSolve the following questions: Q1) Check whether the set W = {(2a + 5b, –a + b, 3a + 4b); a, b are real numbers } is a subspace of R3 or not.arrow_forwardSolve the problem. Find all values of h such that y will be in the subspace of R³ spanned 3] by v1, V2, V3 if v1 = | 2|, v2 =| 4, v3 =| 0, and y = |2|. [-1] -4 -8 O h = -16 all h + -4 O h = -4 or O O h = -4arrow_forward
- From 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_forwardI need help for problem (h). Check that the set at (h) is a subspace of Rn or not.arrow_forwardDiagonalized if possible, where is A=[■(4&0&1@1&1&0@3&0&1)].arrow_forward
- How do I verify that Problem #8 is true? I think that is what it is asking for. Also, this question and many other questions in this section are very much conceptual. Although, the math can be used to verify if each question is true. This specific problem is from a linear algebra textbook called Linear Algebra w/ Applications and the author is by Jeffrey Holt. Right now, I'm in Section 7.1, which consists of what makes a vector space a vector space. Ironically, the author mentioned something new with an R raised to a matrix, as well as a P raised to a number. Nonetheless, I am most certainly not sure of how to answer the problem, but here are some pictures.arrow_forwardProblem 25. Suppose yı (x), y2(x), and y3(x) are three different functions of x. The vector space they span could have dimension 1, 2, or 3. Give an example of y1, y2, y3 for each case.arrow_forwardby Problem 2. Consider the set V = R² with addition and scalar multiplication defined (X1, X2) ℗ (Y1, Y2) = (X1 + X2, Y₁ + y2), a (x₁, x₂) = (ax₁, x₂). Is V a vector space with these operations? Justify your answer.arrow_forward
- Let P(1, 4, −2) and Q(2, 2, 0) be two points in three-dimensional space.arrow_forwardWhich of the following are vector spaces? Justify your answer. (a) The set of all polynomials of degree 3. (b) The set of all vectors x = (x1, x2, x3), satisfying 3x₁ + 5x2 − 9x3 = 2023. (c) The set of all vectors x = (x1, x2, x3), satisfying 2024x₁ + x2 = 0 has a unique solution. (d) The set of all 3 × 3 matrices such that Ax= (e) The set of all n × n (n = N) diagonal matrices. - x3 = 0. -arrow_forwardFor which value of a is the solution set of the following system х+5у +z —D b — 5 2х — 4y — z —а+b-3 | a subspace of R³?arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning