{:a4. Let V = R' and let W|a, b, c, d E Rbe vector spaces over R. Define L: V → W andK :V → W byx +yL:and K:x - y 0w - z-1(a) Prove that L is a linear transformation.(b) Show that K is not a linear transformation.(c) Find ker(L), the kernel of L.

It is given that V=ℝ4 and W=abcd |a,b,c,d∈ℝ be vector space over ℝ. Two functions L:V→W and K:V→W…

а b 4. Let V = R' and let W = {| a |a, b, c, d E R be vector spaces over R. Define L´: V → W and K :V → W by y I +y L: and K: w w – z -1 (a) Prove that L is a linear transformation. (b) Show that K is not a linear transformation. (c) Find ker(L), the kernel of L.

а b 4. Let V = R' and let W = {| a |a, b, c, d E R be vector spaces over R. Define L´: V → W and K :V → W by y I +y L: and K: w w – z -1 (a) Prove that L is a linear transformation. (b) Show that K is not a linear transformation. (c) Find ker(L), the kernel of L.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 16RQ

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Question

{:
a
4. Let V = R' and let W
|a, b, c, d E R
be vector spaces over R. Define L: V → W and
K :V → W by
x +y
L:
and K:
x - y 0
w - z
-1
(a) Prove that L is a linear transformation.
(b) Show that K is not a linear transformation.
(c) Find ker(L), the kernel of L.

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