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Math Help - questions about vectors and basis

  1. #1
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    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
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    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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