Linear Algebra Example Problems - Linear Transformation Ax #1

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.

[adamramondo]

spent like 30 minutes looking at some generalized formulas just to find your video which explains it perfectly in one example. Thank you

[vamonosraza]

Thank you so much for all your Videos!

[MaxUP]

Isn't this just scaling? What about rotation, shearing, and projection?

[oghuvwublessing]

Thank ypu very much, Doc. GOD bless you.

[klodd]

Nice video. One question, how would I do it in "reverse"?
Lets say I want to find the matrix A for the linear transformation T: R3->R3 that is defined by, that the vector u first transforms on v x u where v = (1, 2, 3) and then transforms to the plane x=z?
I hope you understand this, english is not my native language so I dont know all the mathematical terms in english.

[bonniekshow]

I am confused on how you multiplies a 3x3 matrix and 3x1 matrix. I believe there is a mistake somewhere

[ragnarlothbroke]

What do we do when have to have find the values of those a, b and c tho? Like in that last part you did