Provide an appropriate response.
-Which of the following statements are true?
I: Suppose $\mathrm { f } : \mathfrak { R } ^ { \mathrm { n } } \rightarrow R ^ { \mathrm { m } }$ is a linear transformation and $S$ is an affine subset of $R ^ { \mathrm { n } }$. It follows that the set of images $f ( S )$ is an affine subset of $R ^ { m }$.
II: If $A \subset B$, then aff $A \subset B$.
A) I
B) Neither I or II
C) Both I and II
D) II

Question

Quizplus · Accepted Answer

I: True. The image of an affine set under a linear transformation is affine. This is because an affine set can be expressed as $a + V$, where $a$ is a point in the space and $V$ is a subspace. The image of this under a linear transformation $f$ would be $f(a) + f(V)$, where $f(V)$ is still a subspace due to the properties of linear transformations, making the image affine.II: False. The affine hull of $A$ (aff $A$) is the smallest affine set containing $A$, which can extend beyond the boundaries of $B$, even if $A \subset B$.

Provide an Appropriate Response f:Rn→Rm\mathrm { f } : \mathfrak { R } ^ { \mathrm { n } } \rightarrow R ^ { \mathrm { m } }f:Rn→Rm

Provide an Appropriate Response $\mathrm { f } : \mathfrak { R } ^ { \mathrm { n } } \rightarrow R ^ { \mathrm { m } }$