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Math Help - Bases and transition matrix question

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    Bases and transition matrix question

    Let B = {} and B' = {} for two bases in \Re^3, and suppose that the transition matrix from B' to B is

    P = \begin{pmatrix}1 & -1 & 2 \\ 0 & 1 & 2 \\ 3 & 0 & -1 \end{pmatrix}

    find u_1 and u_2 as linear combinations of v_1, v_2, v_3
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  2. #2
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    Quote Originally Posted by flaming View Post
    Let B = {} and B' = {} for two bases in \Re^3, and suppose that the transition matrix from B' to B is

    P = \begin{pmatrix}1 & -1 & 2 \\ 0 & 1 & 2 \\ 3 & 0 & -1 \end{pmatrix}

    find u_1 and u_2 as linear combinations of v_1, v_2, v_3
    B must have 3 elements not 2. let B=\{u_1,u_2,u_3 \}. then u_j=Pv_j, \ 1 \leq j \leq 3. so we have: u_1=v_1-v_2+2v_3, \ u_2=v_2 + 2v_3, \ u_3=3v_1-v_3.
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