Show that the transformation T defined by T(x₁, x₂) = (4x₁2x₂, X₁ +3, 5x₂) is not linear.If T is a linear transformation, then T(0) = 0 and T(cu + dv)=cT(u)+dT(v) for all vectors u, v in the domain of T and all scalars c, d.(Type a column vector.)wrory

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Answered: Show that the transformation T defined…

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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just tell me linear or not linear plz
The cross product of two vectors in R' is defined by 日-屏 [b1 azb3 – azb2 ai a2 b2 azbı – aıb3 b3 aıb2 – azbı аз Let i . Find the matrix A of the linear transformation from R to R° given by T(7) = j x a. A = || ||
Let Pn denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D : P3 - P2 be the function that sends a polynomial to its derivative. That is, D(p(x)) = p' (x) for all polynomials p(x) = P3. Is D a linear transformation? Let p(x) = a³x³ + ²x² + a₁ + a₁ and q(x) = b3x³ + b₂x² + b₁x + b₁ be any two polynomials in P3 and c E R. a. D(p(x) + q(x)) = . (Enter a3 as a3, etc.) D(p(x)) + D(q(x)) = Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) = P3? choose b. D(cp(x)) = + c(D(p(x))) = = Does D(cp(x)) = c(D(p(x))) for all CER and all p(x) = P3? choose ✪ c. Is D a linear transformation? choose ◆
-2 Use a rectangular coordinate system to plot u = ,v = 1, and their images under the 4 -1 given transformation T(x) = | Describe geometrically what T does to each vector in R2.
Let denote the vector space of polynomials in the variable x of degree n or less with real coefficients. Let D: 03 → be the function that sends a polynomial to its derivative. That is, D(p(x)) = p'(x) for all polynomials p(x) E 3. Is D a linear transformation? Let p(x) = a3x³ + a₂x² + a₁x + aº and q(x) = b3x³ + b₂x² + b₁x + bo be any two polynomials in 3 and c E R. a. D(p(x) + q(x)) = D(p(x)) + D(q(x)) = Does D(p(x) + q(x)) = D(p(x)) + D(q(x)) for all p(x), q(x) = ? choose b. D(cp(x)) = c(D(p(x))) = Does D(cp(x)) = c(D(p(x))) for all c ER and all p(x) E 3? choose c. Is D a linear transformation? choose . (Enter a3 as a3, etc.)
Please help solve! Thank you
Let T : R2 → R² be the linear transformation which rotates vectors counter-clockwise about the origin by 7T/3 radians (60 degrees). (i) Find the standard matrix of the linear transformation T. (ii) Use your matrix to rotate the vector v = counterclockwise about the origin by 4 T/3 radians.
Let L be a linear transformation on R2 such that L([1,1]) = ([-2,1]) and L([-1,1]) = [7,-1]. then what's the vector L([7,-1]) sorry to but the numbers in the brackets are in columns, I don't know how to write it thats why.
The cross product of two vectors in R³ is defined by Let ✓ = A = [1] 8 . Find the matrix A of the linear transformation from R³ to R³ given by T(x) = × đ. a2 X b₁ b₂ b3 = [a2b3-a3b₂] | a3b1 — a1b3 [a1b₂-a2b₁]

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Show that the transformation T defined by T(x₁, x₂) = (4x₁2x₂, X₁ +3, 5x₂) is not linear. If T is a linear transformation, then T(0) = 0 and T(cu + dv)=cT(u)+dT(v) for all vectors u, v in the domain of T and all scalars c, d. (Type a column vector.) wrory