38.) With respect to standari basis vectors a lineartransformation T:R* → R³ is given by thematrix3 -1-1- 2 21- 1231The dimension of Ker ('T) is(a) 1(b) 2(d) 4(c) 3

Given T:R4→R3 is given by the matrix 3-1-11-22-2-2-1-131

Answered: 38.) With respect to standari basis…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The standard matrix of the transformation T defined by T(x,,x2,x3)= (x,+2x2,-X3 , 4x, -X3) 1 2 0 -2 0 1 0 4 1 1 2 0 0 0 -1 40 1 1201 0 4 1 40 1 1 2 0 0 0 -1 40 -1 1 2 0 20 -1 14 -1 none
(1) For the following linear transformations T find its matrix representation with respect to the standard basis.
Let T : P2 → M2x2 be the linear transformation defined by T(ax? + bx + c) |0 a (a) Find the matrix for T with respect to the standard bases of P2 and M2x2- (b) Find the matrix for T with respect t B basis for M2x2. {1, x+1, x²+2x+1} and the standard
Let B = {b, b, b3} be a basis for vector space V. Let T: V → V be a linear transformation with the following properties. T(b,) = - 8b, - 6b2: T(b2) = - 2b, +4b2: T(b3) = - 7b, %3D Find [T]B, the matrix for T relative to B.
Let V be a vector space of dim 3 over R let T : V → V be a Linear Transformation 1. -1 given by the matrix A = 1 -4 3 with ordered basis {V1, V2, V3} of V. Then - 2 5 -3 which of the following is TRUE? (a) T(V2) = 0 (c) T(V, + V2 + V3) = 0 (b) T(V1 + V2) =0 . (d) T(V1 + V3) = T(V2) %3D
Let B = {b₁,b2,b3} be a basis for vector space V. Let T: V → V be a linear transformation with the following properties. == T(b₁) = -6b₁ + 5b₂, T(b₂) -3b₁ +4b₂, T (b3) =b₁ 1 Find [T]B, the matrix for T relative to B.
Let T : R³ → R³ be the linear transformation that does the following things, in this order, to an input vector x = [x y z]¹: (i) Interchanges the second and third coordinates of . (ii) Multiplies the first coordinate of the resulting vector by 2. (iii) Replaces the second coordinate of the resulting vector with a 0. (iv) Multiplies the resulting vector by the following matrix: 0 0 0 0 You don't have to show that T is linear. (a) The description of T given above is purely algebraic, in that it explicitly describes how to take 7 = [x y z] and write down T() in coordinates. Give a geometric description of what each of the four "steps" of applying T actually does to a vector. (Your Week 9 tutorials may help in describing what the last step does.) (b) Find the standard matrix AT of T. (c) Find a spanning set for null(AT), and describe what null(AT) is geometrically (i.e., describe it geomet- rically as a subset of R³) (d) Find a spanning set for im(AT), and describe what im(AȚ) is…
Can you please help me with this problem because I don't understand it and can you do it step by step and don't skip any stteps
Asap plz
defined by Let Let ƒ : R² → R² be the linear transformation [f] B = B C f(x) = = = 3 2 -2 - -3 x. be two different bases for R². Find the matrix [f] for f relative to the basis B in the domain and C in the codomain. {(-1,2), (3,-7)}, {{-1, -2), (3, 7)},
1. Let S={[[[7]}

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38.) With respect to standari basis vectors a linear transformation T:R“ → R´ is given by the matrix 1 - 2 2 2 - 1 1 3 1 The dimension of Ker (T) is (a} 1 (c) 3 (b) 2 (d) 4