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Math Help - transition

  1. #1
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    transition

    may i know, given that A is the basis of (a1,a1,a) , B is the basis of )b1,b2,b3)
    is
    b1=a1-a3
    b2=a1-a2
    b3=a1+a1+a3
    the transitition matrix from A to B or from B to A? i thought this was the transition matrix from A to B but the answers in my notes seems to suggest otherwise
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    may i know, given that A is the basis of (a1,a1,a) , B is the basis of )b1,b2,b3)
    is
    b1=a1-a3
    b2=a1-a2
    b3=a1+a1+a3
    the transitition matrix from A to B or from B to A? i thought this was the transition matrix from A to B but the answers in my notes seems to suggest otherwise
    ??? Well, that's NOT a matrix, it is a system of equations. What matrix did you mean?
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  3. #3
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    im trying to solve for the matrix of T in basis B.

    i was given that A is the basis of (a1,a1,a) , B is the basis of )b1,b2,b3)
    and this set of equations
    b1=a1-a3
    b2=a1-a2
    b3=a1+a1+a3.
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  4. #4
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    Quote Originally Posted by alexandrabel90 View Post
    im trying to solve for the matrix of T in basis B.

    i was given that A is the basis of (a1,a1,a) , B is the basis of )b1,b2,b3)
    and this set of equations
    b1=a1-a3
    b2=a1-a2
    b3=a1+a1+a3.
    Are you sure of that last equation? b3= 2a1+ a3?

    Then \begin{bmatrix}b_1 \\ b_2 \\ b_3\end{bmatrix}= \begin{bmatrix}1 & 0 & -1 \\ 1 & -1 & 0 \\ 2 & 0 & 1\end{bmatrix}\begin{bmatrix}a_1 \\ a_2 \\ a_3\end{bmatrix}

    or b3= a1+ a2+ a3?

    Then \begin{bmatrix}b_1 \\ b_2 \\ b_3\end{bmatrix}= \begin{bmatrix}1 & 0 & -1 \\ 1 & -1 & 0 \\ 1 & 1 & 1\end{bmatrix}\begin{bmatrix}a_1 \\ a_2 \\ a_3\end{bmatrix}
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  5. #5
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    sorry it was a typo on my part. its b3= a1+ a2+ a3

    in such a case,
    b1=a1-a3
    b2=a1-a2
    b3=a1+a2+a3 is the transition matrix from basis A to B right?

    let this set of equations above be P.

    in this question, i was also given that T is the linear map whose matrix in basis A is
    (3 4 5 )
    (0 1 -3)
    (2 -1 -2)..let me denote this matrix as A

    then isit right for me to say that

    T(b)=P A P^-1 v(b)

    where T(b) is the matrix of T in B and v(b) is the vector in B..

    thank you!
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  6. #6
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    what im unsure about is that usually, for the questions on these chapters that i have done, the formula that i use is

    T(B) =P^-1 A P v(B)..but in this case, it seems to be the other way round..did i maake a mistake somewhere in my workings?
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