Sub-Task (a). Find a linear mapping F:R³→R³ whose kernel is spanned by ui=(2, 1, 3) and u2=(0,2, 3).Sub-Task (b). Find a basis and the dimension of the KerF.Sub-Task (c). Find a basis and the dimension of the ImF.

I have assumed third vector for which the Combined vectors form basis for R3

Sub-Task (a). Find a linear mapping F:R3→R3 whose kernel is spanned by ui=(2, 1, 3) and uz=(0, 2, 3). Sub-Task (b). Find a basis and the dimension of the KerF. Sub-Task (c). Find a basis and the dimension of the ImF.

Sub-Task (a). Find a linear mapping F:R3→R3 whose kernel is spanned by ui=(2, 1, 3) and uz=(0, 2, 3). Sub-Task (b). Find a basis and the dimension of the KerF. Sub-Task (c). Find a basis and the dimension of the ImF.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...

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Question

Sub-Task (a). Find a linear mapping F:R³→R³ whose kernel is spanned by ui=(2, 1, 3) and u2=(0,
2, 3).
Sub-Task (b). Find a basis and the dimension of the KerF.
Sub-Task (c). Find a basis and the dimension of the ImF.

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