Let T: R³ → R4 be a linear transformation so that T(x)-2-30 1-1A =0010 00Which of the following is/are true?A. The kernel of T is a subspace of R4.B. The range of T is the column space of A.C. The null space of A is the empty set because dim(Nul A) = 0.OA and C onlyOA, B, and C○ C only○ A only○ B onlyAx, where

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Answered: Let T': R³ → R4 be a linear…

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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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.)
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Let T': R³ → R4 be a linear transformation so that T(x) = Ax, where 1 -2 -3 0 1 -1 A = 0 0 1 0 0 0 Which of the following is/are true? A. The kernel of T is a subspace of R4. B. The range of T is the column space of A. C. The null space of A is the empty set because dim(Nul A) = 0. OA and C only