Consider a transformation that accepts a $5-$dimensional vector as an input and produces a $3$dimensional vector as a result. Assuming the transformation is linear:

Write the transformation as an input $/$ output relationship $($i$.$e$.,$ write the function definition$).$

Provide the matrix operation that describes the transformation, highlighting the size of each vector and matrix.

Provide an example for the matrix A that describes the linear transformation. You can show this either with a numerical example, or through a general form without numbers.