jernplate8
2021-01-05
Answered

For each problem below, either prove that the mapping is linear or explain why it cannot be linear.

$1.f({x}_{1},{x}_{2})=(2{x}_{1}-{x}_{2},3{x}_{1}+{x}_{2})$

$2.L(x,y,z)=(x+y,y+z,z+5)$

$3.L(x,y)=(x+y,0,x-2y)$

$4.f(x,y)=(2x+y,-3x+5y)$

$5.f(x,y)=({x}^{2},x+y)$

$6.L(x,y)=(x,x+y,-y)$

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lobeflepnoumni

Answered 2021-01-06
Author has **99** answers

Let V and W be vector spaces, and let

Let V and W be vector spaces, and let

Then for

Therefore ff is a linear transformation.

(3, 4) Try yourself using the definition.

(5) Wheather

(6) Try yourself using the definition.

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