Kernel of Linear TransformationConsider the linear mapping F : Rª → RªF(x, y, z, t) = (x −y+z+t, 2x - 2y+3z + 4t, 3x − 3y+4z + 5t)a. Find a basis and the dimension of the image of F.b. Find a basis and the dimension of hte kernel of the map of F.

Given:The linear transformation F:R4→R4 is defined by:F(x,y,z,t)=(x−y+z+t,2x−2y+3z+4t,3x−3y+4z+5t)…

Answered: Kernel of Linear Transformation…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 5E

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Kernel of Linear Transformation Consider the linear mapping F : Rª → Rª F(x, y, z, t) = (x −y+z+t, 2x - 2y+3z + 4t, 3x − 3y+4z + 5t) a. Find a basis and the dimension of the image of F. b. Find a basis and the dimension of hte kernel of the map of F.