# questions about vectors and basis

• Sep 7th 2009, 12:40 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
• Sep 7th 2009, 08:04 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 \$\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.
• Sep 7th 2009, 08:10 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 \$\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.