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Math Help - Matrix Problem

  1. #1
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    Question Matrix Problem

    I having problem in doing some question and i think the question is out of my level of my matrix. Or maybe the question is quite tricky. So here's the question. There's a formula given for converting fahrenhiet to Celsius C=5/9(F-32). So here the main question. How to construct the above into matrix? I cann't or maybe dont know how to change the formula above to matric. a) the question here is search for 2 times 2 matrix B that transform the vectorMatrix Problem-screenshot_2.png.. Clue here is 2nd row of B is [0 1].
    b)Is the B matrix invertible and if so look for inverse
    c)by using part b result write a formula expresing F in term of C
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  2. #2
    MHF Contributor

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    Re: Matrix Problem

    This is, by the way, an exercise in "projective coordinates" where we represent the point (x) as the pair (x, 1) with the understanding that the pair (a, b) is equivalent to (a/b, 1).
    That allows us to combine both multiplication and addition or subtraction as a single matrix multiplication. For example,
    \begin{bmatrix}a & b \\ 0 & 1\end{bmatrix}\begin{bmatrix}x \\ 1\end{bmatrix}= \begin{bmatrix}ax+ b \\ 1\end{bmatrix}
    a multiplication by a and an addition of b.

    So C= (5/9)(F- 32)= (5/9)F- 160/9, multiplying F by 5/9 and then adding -160/9 can be done by
    \begin{bmatrix}C \\ 1\end{bmatrix}= \begin{bmatrix}\frac{5}{9} & -\frac{160}{9} \\ 0 & 1 \end{bmatrix}\begin{bmatrix}F \\ 1 \end{bmatrix}
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  3. #3
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    Re: Matrix Problem

    projective coordinates? -.- this suck blood.. i dont have any basic on that.. why u saying that (a,b) is equilvalent to (a/b,1)? and where 160 come from?
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