I am self studying linear algebra via the book "No BS Guide to Linear Algebra" and there is this exercise in the book (E2.3).
The chapter containing this problem didn't have any examples of problems like this, it's main focus was on some matrix-vector properties such as the inverse matrix and how it interacts with the matrix-vector product.
Totally at a loss as to what to even search on google to point me in the right direction on this one.
Don't need a blatant answer to this exact problem, but some direction would be fantastic.
Hint: this is really just testing your understanding of how matrix multiplication works: $$\pmatrix{a&c\cr b&d\cr}\pmatrix{v_1\cr v_2\cr} =\pmatrix{av_1+cv_2\cr bv_1+dv_2\cr} =v_1\pmatrix{a\cr b\cr}+v_2\pmatrix{c\cr d\cr}\ .$$