Let H be the planeЗх-3у+2z-0(*)in R³, that is, H={(x, y, z)OR³ | 3x-3y+2z=0} and let F be the linear map, F:R³→R³F(x,Y.Z)=(4x+1y+3z; 2y-2z; (-2)2y+4z).Sub-Task (a). Find F(H)Sub-Task (b). Find F-'(H)

Given, H ={(x, y, z)∈ℝ3| 3x-3y+2z=0}Since, 3x-3y+2z=0⇒x =3y-2z3⇒H =3y-2z3, y, z∈ℝ3| 3x-3y+2z=0…

Let H be the plane Зx-3у+2z-0 (*) in R³, that is, H={(x, y, z)OR³ | 3x-3y+2z=0} and let F be the linear map, F:R³–→R³ F(x.V.2)-(4x+1y+3z; 2y-2z; (-2)2y+4z). Sub-Task (a). Find F(H) Sub-Task (b). Find F-(H)

Let H be the plane Зx-3у+2z-0 (*) in R³, that is, H={(x, y, z)OR³ | 3x-3y+2z=0} and let F be the linear map, F:R³–→R³ F(x.V.2)-(4x+1y+3z; 2y-2z; (-2)2y+4z). Sub-Task (a). Find F(H) Sub-Task (b). Find F-(H)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

Let H be the plane
Зх-3у+2z-0
(*)
in R³, that is, H={(x, y, z)OR³ | 3x-3y+2z=0} and let F be the linear map, F:R³→R³
F(x,Y.Z)=(4x+1y+3z; 2y-2z; (-2)2y+4z).
Sub-Task (a). Find F(H)
Sub-Task (b). Find F-'(H)

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