Let $f\in(\Bbb R^3)^*$ be defined by $f(x_1,x_2,x_3)=x_1+2x_2-x_3$ and $$g:\Bbb R^2\mapsto \Bbb R^3$$ $$(x_1,x_2)\mapsto (3x_1-2x_2,x_2,x_1-2x_2)$$

  1. Determine the matrix $M_{B_2^*\leftarrow B_3^*}(g^*)$ where $B_2^*$ and $B_3^*$ are the standard basis in $\Bbb R^2$ and $\Bbb R^3$

  2. Determine $g^*(f)$

So for a), if g takes something in $\Bbb R^2$ and outputs $\Bbb R^3$, then $g^*$ would take somehting from $\Bbb R^2$ to $\Bbb R$ or from $\Bbb R^3$ to $\Bbb R$? I am not really sure how the lienar functional would look like! Any help appreciated.


If g is a linear function, I.e. $g:\Bbb R^2 \rightarrow \Bbb R^3$, how can it have a dual space ? It’s not a vector space itself...


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.