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Math Help - Find a formula for T^−1 if

  1. #1
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    Find a formula for T^−1 if

    I don't understand how to do this question! Doesn't it just mean to find the inverse of matrix T?

    Find a formula for T^-1 if

    T(x1,x2) = (8x1 - 4x2, 6x1 - 6x2)

    Therefore:

    T^-1(x1,x2) = (_x1 + _x2,_x1 + _x2) ?

    What's the matrix of T...
    Wouldn't it be like:
    [8 -4]
    [6 -6] ?!

    Thank you so much...I'm confused.
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  2. #2
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    Re: Find a formula for T^−1 if

    Hey UBCBOY.

    In terms of the formula, do you know the formula to find the inverse of a 2x2 matrix?
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  3. #3
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    Re: Find a formula for T^−1 if

    in general, if we have the matrix

    A = \begin{bmatrix}a&b\\c&d \end{bmatrix}

    and ad - bc is non-zero, then:

    A^{-1} = \frac{1}{ad - bc}\begin{bmatrix}d&-b\\-c&a \end{bmatrix}.
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  4. #4
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    Re: Find a formula for T^−1 if

    Are you required to use matrices? You are given T in terms of equations, not matrices. From "T(x1,x2) = (8x1 - 4x2, 6x1 - 6x2)"
    you know that y1= 8x1- 4x2 and y2= 6x1- 6x2. Solve those two equations for x1 and x2 in terms of y1 and y2, then, to get the form you want, swap "x" and "y".
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