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Linear Algebra

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Moderate

Scaling Composed with Other Linear Transformations

LINALG-VG9216

Let $M:\mathbb{R}^2\rightarrow\mathbb{R}^2$ be the linear transformation defined by $M(\vec{v})=2\vec{v}$ for all $v\in\mathbb{R}^2$ and let $T:\mathbb{R}^2\rightarrow\mathbb{R}^2$ be any linear transformation. If one defines $D:\mathbb{R}^2\rightarrow\mathbb{R}^2$ by

$$D(\vec{v})=T(M(\vec{v}))-M(T(\vec{v}))$$ then

A

$D(\vec{v})=\vec{v}$ for all $\vec{v}\in\mathbb{R}^2$.

B

$D(\vec{v})=-\vec{v}$ for all $\vec{v}\in\mathbb{R}^2$

C

$D(\vec{v})=0$ for all $\vec{v}\in\mathbb{R}^2$

D

$D(\vec{v})=2\vec{v}$ for all $\vec{v}\in\mathbb{R}^2$

E

$D(\vec{v})=-2\vec{v}$ for all $\vec{v}\in\mathbb{R}^2$