-2
$\begingroup$

Working in $\Bbb R^2$, Find a nonzero vector v and ordered bases B and B' such that $[v]_B$ = $[v]_{B'}$ , but B $\neq$ B'

Could someone explain and give an example?

  • 0
    Hi, on this site you're supposed to show what you have tried so far. – 2017-02-17
  • 0
    There are other ways to provide context, apart from "show what you have tried". Where did you encounter this problem? Why is it interesting to you? Like sharing your attempt to solve the problem, these other forms of context help Readers to respond in a way you are likely to find helpful. – 2017-02-17

2 Answers 2

2

Take $B = (e_1, e_2), B' = (e_2, e_1), v = e_1+e_2$.

Also, $B' = (-e_1,2e_1+e_2)$.

In both cases, $[v]_B = (1,1) = [v]_{B'}$.

1

Hint:

If $B=\{v_1,v_2\}$ you can take $v_1$ as an element of the basis $B'$....