For each of the following linear transformations of the plane IR², determine where the transformation sends e, and e2, writing your answers as linear combinations of e, and e₂. Enter exactvalues, not decimal approximations.(A) A horizontal shear that transforms e₂ into ₂ - 3e₁ (leaving ₁ unchanged).e₁+→e₂ →e₁ He₂ →(B) Rotation of the plane counter-clockwise about the origin by radians.e₁+e₂ He₁+(C) Reflection of the plane through the line y = -2.е₁ →e₁+e₂ →e₁+What is the standard matrix for T?e₂e₁+€₂e₁+€₂$e₁+(D) The composite linear transformation T that first performs (A), then performs (B), and finally performs (C).e₂ →e₂$e₂€₂e₂

We know that, Standard basis of R2 e1 = (1,0) e2 = (0,1)

For each of the following linear transformations of the plane IR", determine where the transformation sends e, and eż, writing your answers as linear combinations of e, and ez. Enter exact values, not decimal approximations. (A) A horizontal shear that transforms e₂ into ₂-3e₁ (leaving e₁ unchanged). e₁ H e₁+ C₂H e₁+ (B) Rotation of the plane counter-clockwise about the origin by radians. e₁+ CH e₂ → e₁+ (C) Reflection of the plane through the line y = -2. e₁+ e₁+ (D) The composite linear transformation T that first performs (A), then performs (B), and finally performs (C). e₁ → e₁+ e → e₂ What is the standard matrix for T'? e₁+ e₂ e₂ e₂

For each of the following linear transformations of the plane IR", determine where the transformation sends e, and eż, writing your answers as linear combinations of e, and ez. Enter exact values, not decimal approximations. (A) A horizontal shear that transforms e₂ into ₂-3e₁ (leaving e₁ unchanged). e₁ H e₁+ C₂H e₁+ (B) Rotation of the plane counter-clockwise about the origin by radians. e₁+ CH e₂ → e₁+ (C) Reflection of the plane through the line y = -2. e₁+ e₁+ (D) The composite linear transformation T that first performs (A), then performs (B), and finally performs (C). e₁ → e₁+ e → e₂ What is the standard matrix for T'? e₁+ e₂ e₂ e₂

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 46E: For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T...

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