0
$\begingroup$

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).

enter image description here

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.

$\endgroup$
2
  • 2
    $\begingroup$ Hint: $Ev$ is a linear combination of columns of $E.$ $\endgroup$ Commented Jan 4, 2023 at 3:21
  • $\begingroup$ $Ev = v_1 e_1 + v_2 e_2$. $\endgroup$
    – copper.hat
    Commented Jan 4, 2023 at 4:09

1 Answer 1

2
$\begingroup$

Hint: this is really just testing your understanding of how matrix multiplication works: $$\pmatrix{a&c\cr b&d\cr}\pmatrix{v_1\cr v_2\cr} =\pmatrix{av_1+cv_2\cr bv_1+dv_2\cr} =v_1\pmatrix{a\cr b\cr}+v_2\pmatrix{c\cr d\cr}\ .$$

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .