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FP1 Invariant Points Help Required Watch

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    The matrix T maps 

\begin{pmatrix} x \\ y \end{pmatrix} onto

    

\begin{pmatrix} a & c \\ b & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}

Hence show that invariant points other than the origin exist if Det(T) = a + d -1. I said that x = ax + cy and  y= bx + dy and that therefore a=1, c=0, b=0, d=1. I don't understand how I can find the determinate of T from this.
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    (Original post by Shipreck)
    The matrix T maps 

\begin{pmatrix} x \\ y \end{pmatrix} onto

    

\begin{pmatrix} a & c \\ b & d \end{pmatrix} *

\begin{pmatrix} x \\ y \end{pmatrix}

    Unparseable or potentially dangerous latex formula. Error 6: Image was not produced or one of its dimensions is too small.
    wat
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    (Original post by RDKGames)
    wat
    Pressed submit while still figuring the latex out. Lmao sorry.
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    (Original post by RDKGames)
    wat
    fixed
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    (Original post by Shipreck)
    The matrix T maps 

\begin{pmatrix} x \\ y \end{pmatrix} onto

    

\begin{pmatrix} a & c \\ b & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}

Hence show that invariant points other than the origin exist if Det(T) = a + d -1. I said that x = ax + cy and  y= bx + dy and that therefore a=1, c=0, b=0, d=1. I don't understand how I can find the determinate of T from this.
    If you solve the simultaneous equations that you have set out as

     \displaystyle x = ax + cy
    \displaystyle  y= bx + dy

    and crunch the algebra, you should arrive at the equation

     \displaystyle ad - bc = a + d - 1

    The left hand side of this is the determinant of T.
 
 
 
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