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-2), V1 in R³. - 40. If p₁(x) = x − 4 and p2(x) = x² − x + 3, determine whether p(x) = 2x² - x + 2 lies in span{p₁, P2}. 41. Consider the vectors 1, 2), V2 A1 A₁ = 30 4-[2-1)]-*-[-2] -4 - [39] A2 A₂ = A3 = 12 01

-2), V1 in R³. - 40. If p₁(x) = x − 4 and p2(x) = x² − x + 3, determine whether p(x) = 2x² - x + 2 lies in span{p₁, P2}. 41. Consider the vectors 1, 2), V2 A1 A₁ = 30 4-[2-1)]-*-[-2] -4 - [39] A2 A₂ = A3 = 12 01

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 41CR: Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the...
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Solve #40, SHOW every step of your work and explain. DO NOT TYPED IT, POST PICTURES OF YOUR WORK!

be the subspace of M2 (R) consisting of all 2 matrices whose four elements sum to zero (see lem 12 in Section 4.3). Find a set of vectors that s S. S be the subspace of M3 (R) consisting of all 3 matrices such that the elements in each row and column sum to zero. Find a set of vectors that s S. S be the subspace of M3 (R) consisting of all 3 × 3 metric matrices. Find a set of vectors that spans S. be the subspace of R³ consisting of all solutions e linear system x - 2yz = 0. rmine a set of vectors that spans S. 5 be the subspace of P3 (R) consisting of all poly- ials p(x) in P3 (R) such that p'(x) = 0. Find a set ectors that spans S. ms 25-33, determine a spanning set for the null e given matrix A. matrix A defined in Problem 23 in Section 4.3. matrix A defined in Problem 24 in Section 4.3. matrix A defined in Problem 25 in Section 4.3. For Problems 37-39, determine whether the given vector v lies in span{V₁, V2}. 37. v = (3, 3, 4), v₁ = (1, −1, 2), v₂ = (2, 1, 3) in R³. 38. v = (5, 3, −6), v₁ = (−1, 1, 2), v₂ = (3, 1, −4) in R³. 39. v = (1, 1, -2), v₁ = (3, 1, 2), v2 = (-2,-1, 1) V1 in R³. 40. If p₁(x) = x − 4 and p2(x) = x² - x +3, determine whether p(x) = 2x² − x + 2 lies in span{p₁, P2}. - 41. Consider the vectors 1 01 30 A1 1 = [2 -1] - 4² - [ 2 ] -4 = [²2] A2 = A3 0 -2 1 12 in M₂ (R). Determine span{A1, A2, A3}. 42. Consider the vectors A1 12 -2 -[-] 42 = [1-4] A2 9 -1 3 = in M₂ (R). Find span{A₁, A2}, and determine whether 3 1 or not B = 41 lies in this subspace. -2 4
Transcribed Image Text:be the subspace of M2 (R) consisting of all 2 matrices whose four elements sum to zero (see lem 12 in Section 4.3). Find a set of vectors that s S. S be the subspace of M3 (R) consisting of all 3 matrices such that the elements in each row and column sum to zero. Find a set of vectors that s S. S be the subspace of M3 (R) consisting of all 3 × 3 metric matrices. Find a set of vectors that spans S. be the subspace of R³ consisting of all solutions e linear system x - 2yz = 0. rmine a set of vectors that spans S. 5 be the subspace of P3 (R) consisting of all poly- ials p(x) in P3 (R) such that p'(x) = 0. Find a set ectors that spans S. ms 25-33, determine a spanning set for the null e given matrix A. matrix A defined in Problem 23 in Section 4.3. matrix A defined in Problem 24 in Section 4.3. matrix A defined in Problem 25 in Section 4.3. For Problems 37-39, determine whether the given vector v lies in span{V₁, V2}. 37. v = (3, 3, 4), v₁ = (1, −1, 2), v₂ = (2, 1, 3) in R³. 38. v = (5, 3, −6), v₁ = (−1, 1, 2), v₂ = (3, 1, −4) in R³. 39. v = (1, 1, -2), v₁ = (3, 1, 2), v2 = (-2,-1, 1) V1 in R³. 40. If p₁(x) = x − 4 and p2(x) = x² - x +3, determine whether p(x) = 2x² − x + 2 lies in span{p₁, P2}. - 41. Consider the vectors 1 01 30 A1 1 = [2 -1] - 4² - [ 2 ] -4 = [²2] A2 = A3 0 -2 1 12 in M₂ (R). Determine span{A1, A2, A3}. 42. Consider the vectors A1 12 -2 -[-] 42 = [1-4] A2 9 -1 3 = in M₂ (R). Find span{A₁, A2}, and determine whether 3 1 or not B = 41 lies in this subspace. -2 4
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