(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Some matrix transformations [itex] f [/itex] have the property that [itex] f(u) = f(v), when u ≠v [/itex]. That is, the images of different vectors can be the same. For each of the following matrix transformations [itex] f : R^{2} → R^{2} [/itex] defined by [itex]f(u) = Au [/itex], find two different vectors [itex] u [/itex] and [itex] v[/itex] such that [itex] f(u)=f(v)=w[/itex] for the given vector [itex] w[/itex].

A = [tex]

\begin{pmatrix}

1 & 2 & 0\\

0 & 1 & -1\\

\end{pmatrix}

[/tex]

w=

[tex]

\begin{pmatrix}

0\\

-1\\

\end{pmatrix}

[/tex]

2. Relevant equations

My professor noted that there was a typo in the book, and that instead of [itex] f : R^{2} → R^{2} [/itex], it should be [itex] f : R^{3} → R^{2} [/itex].

3. The attempt at a solution

My professor has been on jury duty for the past week, and our sub just assigns us homework without much instruction or guidance. We haven't been properly introduced to the notation [itex] R[/itex], either.

But from inferring from the problem, is it safe to assume that [itex] w = Au [/itex]?

Also, would I have to use something along the lines of

u = [tex]

\begin{pmatrix}

x\\

y\\

z\\

\end{pmatrix}

[/tex] ?

Detailed instruction would be much appreciated, as I am anxious to grasp the subject matter.

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# Homework Help: Linear Algebra: Matrix Transformations

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