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# 4.3 Using Matrices for Transformations and its Inverse

#### Using Matrices for Transformations

• Some transformations can be represented as matrices. For instance, all linear transformations can be shown by matrices.

Note: Linear transformation is a general type of transformation that will not be studied in this course. Reflection and dilation are actually particular types of linear transformation, while translation is not.

• Generally, linear transformations (which includes reflection and translation) can be described as:

\left[\begin{array}{l} x \\y\end{array}\right] \rightarrow\left[\begin{array}{ll}a & b \\c & d\end{array}\right]\left[\begin{array}{l}x \\y\end{array}\right]=\left[\begin{array}{l}a x+b y \\c x+d y\end{array}\right]

which describes the rule (x,\ y) \rightarrow(a x+b y,\ c x+d y).

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