6. 'The mapping T :R³ → R? is defined as T (x, y, z) = (x + 2y+ 3z, x + 3y + 2z) is a linear transformation from R³ into R2. Then %3D its Kernel T is (a) L{a} where a = (- 1, 5, 1) (b) L{a} where a = (- 1, 1, 5) %3D (c) L{a} where a = (- 5, 1, 1) (d) None of these

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...
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6. 'The mapping T :R³ → R² is defined as
T (x, y, z) = (x + 2y+ 3z, x + 3y + 2z)
is a linear transformation from R³ into R². Then
%3D
its Kernel T is
(a) L {c} where a = (- 1, 5, 1)
(b) L{a} where a = (- 1, 1, 5)
(ç) L{a} where a = (- 5, 1, 1)
(d) None of these
Transcribed Image Text:6. 'The mapping T :R³ → R² is defined as T (x, y, z) = (x + 2y+ 3z, x + 3y + 2z) is a linear transformation from R³ into R². Then %3D its Kernel T is (a) L {c} where a = (- 1, 5, 1) (b) L{a} where a = (- 1, 1, 5) (ç) L{a} where a = (- 5, 1, 1) (d) None of these
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