# questions about vectors and basis

• September 7th 2009, 01:40 AM
shenpingping
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
• September 7th 2009, 09:04 AM
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 $v_1= <3, 6>$ and $v_2= <-1, 0>$ and are asked to write x= <17, 13> in terms of the basis $\{v_1, v_2\}$. What that means is find coefficents $c_1$ and $c_2$ so that $c_1<3, 6>+ c_2<-1, 0>= <17, 13>$. That gives you two equations to solve for $c_1$ and $c_2$. Can you do that.
• September 7th 2009, 09:10 AM
shenpingping
Quote:

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