Linear Algebra Example Problems – Linear Transformation Ax #1

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In general we note the transformation of the vector x as T(x). We can think of this as the transformation operator “acting on” the vector x to yield a new vector T(x). In general, the number of elements in x and T(x) can be different (i.e. x could be a vector in R3 while T(x) is a vector in R2).

Linear transformations are a special type of transformation, and as such, satisfy certain properties. Linear transformations always have a matrix representation.

In this problem we consider a linear transformation that takes vectors from R3 and returns a vector in R3. The matrix representation of this linear transformation is provided and we compute T(x) for several different values of x.

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