Consider linear transformation F:R4R³ given byF(w, x, y, z)=(w-3x+2y-z, x-y+z, w+y-z)a)b)c)d)Find the standard matrix A for the transformation F.Find the basis kernel of F.Find the nullity (F) and rank (F).Is F one-to-one? Give a reason for your answer.

Given : F : ℝ4 → ℝ3 be a linear transformation defined as ; F(w, x, y, z) = (w-3x+2y-z,…

Answered: Consider linear transformation F: R4 →…

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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Consider linear transformation F: R4 → R³ given by a) b) c) d) F(w, x, y, z)=(w-3x+2y-z, x−y+z, w+y−z) Find the standard matrix A for the transformation F. Find the basis kernel of F. Find the nullity (F) and rank (F). Is F one-to-one? Give a reason for your answer.