Finding out the transformation matrix

[H.Bisho18]

I've recently started on matrices and I'm struggling to figure out how to answer this.


I tried findout out if its reflected in a line or rotated but didn't end up with anything, looking at the answer i can't see how it would relate either

thanks

 

[tkhunny]

Can you write an arbitrary transition matrix?

 

[pka]

I've recently started on matrices and I'm struggling to figure out how to answer this.
View attachment 13721

Can you solve for \(\displaystyle a,b,c,d~?\)
\(\displaystyle \left( {\begin{array}{*{20}{c}} a&b \\ c&d \end{array}} \right)\left( {\begin{array}{*{20}{c}} 2 \\ 0 \end{array}} \right) = \left( {\begin{array}{*{20}{c}}
6 \\ { - 2} \end{array}} \right)\)

\(\displaystyle \left( {\begin{array}{*{20}{c}} a&b \\ c&d \end{array}} \right)\left( {\begin{array}{*{20}{c}} 1 \\ -1 \end{array}} \right) = \left( {\begin{array}{*{20}{c}}
5 \\ { - 1} \end{array}} \right)\)