The matrix M is defined by:
\begin{bmatrix}
-1 & -1 \\
1 & -1 \\
\end{bmatrix}
Assuming the matrix represents an enlargement followed by a rotation
My idea here was to make an equation so you're left with simultaneous equations to solve.
$\begin{bmatrix}
\cos \left(θ\right) & \sin \left(θ\right) \\
-\sin \left(θ\right) & \cos \left(θ\right) \\
\end{bmatrix}
\begin{bmatrix}
x & 0 \\
0 & x \\
\end{bmatrix}
=
\begin{bmatrix}
-1 & -1 \\
1 & -1 \\
\end{bmatrix}$
$\begin{bmatrix}
x\cos \left(θ\right) & x\sin \left(θ\right) \\
-x\sin \left(θ\right) & x\cos \left(θ\right) \\
\end{bmatrix}
=
\begin{bmatrix}
-1 & -1 \\
1 & -1 \\
\end{bmatrix}$
This is where I get stuck. I don't think you can solve this problem like this but if you can, please answer. Regards
A couple more questions,
Does the type of enlargement and type of rotation alter this method? e.g. a scale factor more or less than 1 and a clockwise or counter clockwise rotation.
Also if there is an easier method to finding the matrices could someone please answer with working?
Regards Tom
Best Answer
Looking at determinants, we find $x^2=2$, so if at all, we should have $x=\sqrt 2$.