Determine which of the following transformations are linear transformations.A. The transformation T defined by T(x1, x2, x3) = (x1, x2, —X3)OB. The transformation T defined by T(1, 2, 3) = (1, 2, 3)OC. The transformation T defined by T(1, 2) = (2x₁ − 3x2, x₁ + 4, 5x₂).(4x1 – 2x2,3|x2|).D. The transformation T defined by T(x1, x₂)O E. The transformation T defined by T(x1, x2,=3) = (x1,0, x3)

A transformation is linear if Tx1+y1, x2+y2, x3+y3=Tx1, x2, x3+Ty1, y2, y3. Notice that only the…

Determine which of the following transformations are linear transformations. A. The transformation T defined by T(x1, x2, x3) = (x1, x2, —X3) OB. The transformation T defined by T(x1, x2, 3) = (1, 2, 3) C. The transformation T defined by T(x1, x2) = (2x1 − 3x2, x1 + 4,5x₂). - T defined by T(x1, x2) = (4x1 − 2x2,3|x2|). (x1, 0, x3) D. The transformation E. The transformation T defined by T(x1, x2, x3) =

Determine which of the following transformations are linear transformations. A. The transformation T defined by T(x1, x2, x3) = (x1, x2, —X3) OB. The transformation T defined by T(x1, x2, 3) = (1, 2, 3) C. The transformation T defined by T(x1, x2) = (2x1 − 3x2, x1 + 4,5x₂). - T defined by T(x1, x2) = (4x1 − 2x2,3|x2|). (x1, 0, x3) D. The transformation E. The transformation T defined by T(x1, x2, x3) =

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

(a) Evaluate S(3, 1, −2). (b) Evaluate S(S(3, 1, −2)). (c) Evaluate S(2a, 3a + b, b − 2a), where a and b are arbitrary real numbers.
Determine which of the following transformations are linear transformations. |A. The transformation T defined by T(x1, x2, x3) = (1, x2, x3) B. The transformation T defined by T(x1, x2, x3) = (x1,0, x3) C. The transformation T defined by T(x1, x2, x3) = (x1, x2, -x3) D. The transformation T defined by T(x1, x2) = (4x1 – 2x2, 3|x2|). E. The transformation T defined by T(x1, X2) = (2x1 – 3x2, x1 + 4,5x2).
Suppose that T is a linear transformation such that Write T as a matrix transformation. For any T([¹]) - D, T(3)-441, [], = 7 R2, the linear transformation T is given by T(7) v.
Let T : P2 → P, be the linear transformation such that T(2x) = 2x? – 3x, T(0.5x – 4) = -2x – 4x + 3, T(4x² + 1) = –4x + 4. %3D Find T(1), T(x), T(x²), and T(ax² + bx + c), where a, b, and c are arbitrary real numbers. T(1) = T(x) = T(x²) = T(ax? + bx + c) =
Determine which of the following transformations are linear transformations. A. The transformation T defined by T(1, 2, X3) = (x1,0, X3) B. The transformation T defined by T(x1, x2, 3) = (x1, x2, -3) C. The transformation T defined by T(1, 2, 3) = (1, 2, 3) D. The transformation T defined by T(x₁, x2) = (2x1 - 3x2, x1 +4,5x₂). E. The transformation T defined by T(x₁, x2) = (4x₁ − 2x2, 3|x₂|). -
Consider the following three transformations from R³ to R³: x1 T x2 x1 - 2x3 2x1 - 2x2 - 5x3 x1 x1+5 x1 S x2 x2 R x2 = 0 X3 -x1 + 2x2+8x3) x3 x1x3 X3 Which of these transformations is/are linear? Select all correct choices. T S R None of these
2. Determine whether the mapping T : R4 → R³ defined by X1 2.x1 + 3x4 – 1 X2 T x2 + 5x3 X3 X4 is a linear transformation. Explain your answer.
Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.) a U= [H V = 4 a =
Each of J, K, L, M and N is a linear transformation from R2 to R². These functions are given as follows: J(x1, x2) = (3x1 – 5x2, –6x1 + 10x2), K(x1, x2) = (-V3x2, V3x1), L(x1, x2) = (x2, –x1), M(x1, x2) = (3x1+ 5x2, 6x1 – 6x2), N(x1, x2) = (-V5x1, /5x2).
The vectors u = True O False The vectors u = O True False i 2i 1- i 2 2 2i 1- i -4 and v = and v = [1- 1 + i i i | 1 – 1 + i i i are orthogonal. are orthogonal.