e2 Show that S and T are both linear transformations

topsquark

Forum Staff
Jan 2006
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Wellsville, NY
$$ST\begin{bmatrix}x\\y\end{bmatrix}
=S\left(T\begin{bmatrix}x-4y\\3x\end{bmatrix}\right)
=\left[\begin{array}{c}2(x-4y)+3x \\ x-4y-3x \end{array}\right]$$

do you mean this?
Yes. The term ST is, in fact, a multiplication as Plato pointed out. You really do need to write it as \(\displaystyle S \circ T\).

On the other hand I've never seen the composition symbol used in any of the Physics classes I've taken. So if you are doing Math do it as Plato (or your instructor) says. Otherwise ask your instructor.

-Dan