Linear Algebra Example Problems – Linear Transformation Ax #1

Course website:

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.

If you enjoyed my videos please “Like”, “Subscribe”, and visit to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!


%d bloggers like this: