Finding and using the matrix of a linear transformation relative to non standard bases

[@shreyupalley1767]

hahhahah didnt expect that ending. love it :))

[@santiagocortes7964]

thanks to you i can do my linear algebra homework

[@peakyblinders3365]

What is the real life application of this tho? thanks btw.

[@davidfriday7498]

As a pure mathematician, my obligatory answer is "I don't care." However, especially in physics when problems require a rotation of a coordinate system, I have little doubt in my mind that an application exists. Come to think of it, there are probably applications in the field of double and triple integrals with the associated Jacobians of the transformations into non-standard bases. However, those don't necessarily have to be linear.

[@libelldrian173]

Thanks David! This was a nice exercise tackling several closely related problems that often get confused with one another. Similar problems are often state with ambiguity, for example, I wasn't sure at the beginning if you meant to write the vector v =(2,4,6) with respect to the standard basis or B.