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 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...

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