Show that the transformation T defined by T(X₁, X₂) = (4x₁ − 2X₂, X₁ + 4, 5x₂) is not linear. If T is a linear transformation, then T(0) = 0 T(0,0) = (4(0)-2(0), (0) + 4, 5(0)) =0.0.0 and T(cu + dv)=cT(u) + dT (v) for all vectors u, v in the domain of T and all scalars c, d. (Type a column vector.) Check if T(0) follows the correct property to be linear. Substitute. Simplify.
Show that the transformation T defined by T(X₁, X₂) = (4x₁ − 2X₂, X₁ + 4, 5x₂) is not linear. If T is a linear transformation, then T(0) = 0 T(0,0) = (4(0)-2(0), (0) + 4, 5(0)) =0.0.0 and T(cu + dv)=cT(u) + dT (v) for all vectors u, v in the domain of T and all scalars c, d. (Type a column vector.) Check if T(0) follows the correct property to be linear. Substitute. Simplify.
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 16CM
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![Show that the transformation T defined by T(X₁, X₂) = (4x₁ − 2X₂, X₁ + 4, 5x₂) is not linear.
If T is a linear transformation, then T(0) =
0
T(0,0) = (4(0)-2(0), (0) + 4, 5(0))
= 0.00)
and T(cu + dv)=cT(u) + dT (v) for all vectors u, v in the domain of T and all scalars c, d.
(Type a column vector.)
Check if T(0) follows the correct property to be linear.
Substitute.
Simplify.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F594a73fa-142a-4034-897a-cd9383fc5058%2F23b752a7-8cf7-4c09-a937-0a8035b57b67%2Flt58vo3_processed.png&w=3840&q=75)
Transcribed Image Text:Show that the transformation T defined by T(X₁, X₂) = (4x₁ − 2X₂, X₁ + 4, 5x₂) is not linear.
If T is a linear transformation, then T(0) =
0
T(0,0) = (4(0)-2(0), (0) + 4, 5(0))
= 0.00)
and T(cu + dv)=cT(u) + dT (v) for all vectors u, v in the domain of T and all scalars c, d.
(Type a column vector.)
Check if T(0) follows the correct property to be linear.
Substitute.
Simplify.
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