1. ## questions about vectors and basis

Hi there,

These questions are my assignment, I have tried my best, but could not figure out a hint. Could you please help? Thanks

cheers,
pingping

2. Since you have tried your best, how about showing <b>what</b> you tried so we will know better how to help?

You are given vectors $\displaystyle v_1= <3, 6>$ and $\displaystyle v_2= <-1, 0>$ and are asked to write x= <17, 13> in terms of the basis $\displaystyle \{v_1, v_2\}$. What that means is find coefficents $\displaystyle c_1$ and $\displaystyle c_2$ so that $\displaystyle c_1<3, 6>+ c_2<-1, 0>= <17, 13>$. That gives you two equations to solve for $\displaystyle c_1$ and $\displaystyle c_2$. Can you do that.

3. Originally Posted by HallsofIvy
Since you have tried your best, how about showing <b>what</b> you tried so we will know better how to help?

You are given vectors $\displaystyle v_1= <3, 6>$ and $\displaystyle v_2= <-1, 0>$ and are asked to write x= <17, 13> in terms of the basis $\displaystyle \{v_1, v_2\}$. What that means is find coefficents $\displaystyle c_1$ and $\displaystyle c_2$ so that $\displaystyle c_1<3, 6>+ c_2<-1, 0>= <17, 13>$. That gives you two equations to solve for $\displaystyle c_1$ and $\displaystyle c_2$. Can you do that.
Thank you for your reply, I have solved the above problem. but the other question is unsolved. I do not know where to start. I think I should find the basis for the subspace and then do a orthogonal projection. but not sure how to find the basis. Please help, thanks.