questions about vectors and basis

**shenpingping** · September 7th 2009, 12:40 AM

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

**HallsofIvy** · September 7th 2009, 08:04 AM

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.

**shenpingping** · September 7th 2009, 08:10 AM

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.

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