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).

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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.

  • 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


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


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