(1 point) Which of the following operators in R are linear? |(10,9,8)7 A. L(x) В. L(x)...
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21. Let T be a linear transformation from P2 into P3 over R defined by T(p(x)) xp(x). (a) Find [T]B.A the matrix of T relative to the bases A = {1-x, l-x2,x) and B={1,1+x, 1 +x+12, 1-x3}. (b) Use [TlB. A to find a basis for the range of T. (c) Use TB.A to find a basis for the kernel of T. (d) State the rank and nullity of T.
21. Let T...
(1 point) Consider a linear transformation 7 from Rto R' for which *([]) = 13) and 7 a r (181) - 133 Find the matrix A of T.
Let x = [xı x2 x3], and let TER → R be the linear transformation defined by T() = x1 + 6x2 – x3 -X2 X1 + 4x3 Let B be the standard basis for R2 and let B' = {V1, V2, V3}, where 7 7 and v3 = 7 V1 V2 [] --[] 0 Find the matrix of I with respect to the basis B. and then use Theorem 8.5.2 to compute the matrix of T with respect to...
Question 7 (1 point) Which of the following is the dominant pattern of governance used by transnational firms? O A) Localized OB) Decentralized OC) Duplicated OD) Centralized E) Federal structure Question 8 (1 point) Е в т ү о т о р Η ον Β Ν Μ
Linear Aljebra
Let B = {vy, V2, V3) be a basis for R in which we have and V3 Also, let TR-R be the linear operator such that: T(v.) = T(v2) and T(v.) = -0 X1 Part (a): Find a formula for T X₂ X, Answer: T X2 -0 [Ogg 912 943 = A x2 where A = 421 422 423 х3 231 232 233 Xz 0 } then find the following: Now let the vector w= Part (b): Find...
(1 point) Let T be a linear transformation. Which of the following statements could be used to describe 77 (Select all that apply.) A. T(0) = 0 B. The columns of T are linearly independent. c. T is not empty. D. The domain of Tis R'. E. T contains (ie.. ). E T is a 3 x 4 matrix. G. T is one-to-one.
Which of the following transformations T R2 → R is linear? A. T(x,y)=5 OB. T(x,y) = x2 OC. None of the given options OD. TIX.Y)=3x+4y OE. T(x,y) = x2 + y2
(1 point) Let L be the linear operator in R? defined by L(x) = (4x1 – 2x2, -6x1 + 3x2) Find bases of the kernel and image of L. 00 Kernel: * Image: [-2,3] To enter a basis into WebWork, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is 1 2,1l/, then you would enter [1,2,3], 31 [1,1,1) into the answer blank.
(1 point) For the linear system c(t1 61 X' = AX, with X(t) = A = and X(0) = g(t) (6 -6 - 4 (a) Find the eigenvalues and eigenvectors for the coefficient matrix. L X1 = , X1= * , and 12 = - ,X - = (b) Write the solution of the initial-value problem in terms of X(t), y(t) x(t) = g(t) =
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[4 pts] Problem 2. Verify that is a solution of the partial differential equation Uzr+ Uyy = 5 ptsl Problem 3. (a) Verify that |T, — т 21-Z Y2 y 22 - z= 0 Уз — у 23 — 2 Тз — Т is an equation for the plane through the three noncollinear points P(x1, yi, z1), Q(x2, V2, 2),R(x3, ^3, Z3) (b) Use vectors to verify that the distance from...