5. [-/5 Points] DETAILS LARLINALG8 4. 1.041. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, -1). (Enter your answer in terms of u and w. If not possible, enter IMPOSSIBLE. ) v = (2, 1) V : Need Help? Read It Watch It 6. [-/5 Points] DETAILS LARLINALG8 4.3.032. MY NOTES ASK YOUR TEACHER Determine whether the subset of M, is a subspace of My, with the standard operations of matrix addition and scalar multiplication. The set of all n x n matrices A that commute with a given matrix 8; that is, AB = BA O subspace O not a subspace Need Help? Read It 7. [-/5 Points] DETAILS LARLINALG8 4.2.017. MY NOTES ASK YOUR TEACHER Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set of all first-degree polynomial functions ax, a # 0, whose graphs pass through the origin with the standard operations O The set is a vector space. O The set is not a vector space because it is not closed under addition. O The set is not a vector space because an additive identity does not exist. O The set is not a vector space because an additive inverse does not exist. O The set is not a vector space because the distributive property of scalar multiplication is not satisfied. Need Help? Read It1. [-/5 Points] DETAILS LARLINALG8 4.3.501.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Is w a subspace of V? Assume that V has the standard operations. W is the set of all functions that are differentiable on [0, 5]. V is the set of all functions that are continuous on [0, 5]. O w is a subspace of V. O W is not a subspace of V. Need Help? Read It Submit Answer 2. [-/5 Points] DETAILS LARLINALG8 4. 1.053. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use a software program or a graphing utility with matrix capabilities to write v as a linear combination of uj, U2, ug, u4, and us. Then verify your solution. (Enter your answer in terms of uj, U2, Ug, u4, and us.) v = (5, 2, -9, 11, 8) U1 = (1, 2, -3, 4, -1) U2 = (1, 2, 0, 2, 1) U3 = (0, 1, 1, 1, -4) U4 = (2, 1, -1, 2, 1) us = (0, 2, 2, -1, -1) Need Help? Read It Watch It8. [-/5 Points] DETAILS LARLINALG8 4.1.501.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use a graphing utility or computer software program with matrix capabilities to write v as a linear combination of uj, U2, Ug, u4, us and up. Then verify your solution. u1 = (1, 3, -1, -1, 1, 4) U2 = (4, -1, 1, -3, 4, 3 ) U3 = (3, 4, -3, -2, -2, 2) u4 = (3, 4, -1, 1, 2, 1) Us = (3, -2, -2, 4, -3, 4) us = (1, 3, -2, 1, 2, 4 ) v = (-5, 49, -5, -23, 27, 9) V = Need Help? Read It 9. [-/5 Points] DETAILS LARLINALG8 4. 1.038. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Solve for w where u = (0, -1, 1, 1) and v = (-1, 3, 0, 2). w + 2v = -3u W : Need Help? Read It3. [-/5 Points] DETAILS LARLINALG8 4.2.029. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Determine whether the set, together with the indicated operations, is a vector space. If it is not, then identify one of the vector space axioms that fails. The set of all 4 x 4 matrices of the form OCbc bocc 2 2 0 a bab1 . with the standard operations O The set is a vector space. O The set is not a vector space because it is not closed under addition. The set is not a vector space because it does not satisfy the associative property of addition. O The set is not a vector space because a scalar identity does not exist. O The set is not a vector space because it does not satisfy the distributive property. Need Help? Read It Watch It 4. [-/10 Points] DETAILS LARLINALG8 4.4.001. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, -1, 3), (5, 0, 4)} (a) z = (7, -6, 14) Z = )$1 + ( (b) v = 13 , - 1, 43 $1 + W = (4, -7, 13) W = )$1 + 'd) u = (9, 1, -1) u = )$2 + ( 1 ) $2