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Homework Help: Standard Matrix of Linear Transformation

  1. Apr 3, 2012 #1
    1. The problem statement, all variables and given/known data

    Let T: R3-->R3, defined by T(x)= a x x
    Give the standard matrix A of T, and explain why A is skew-symmetric.

    2. Relevant equations

    They define u x v as

    u x v=(det [u2 u3/ v2 v3], det [u3 u1 /v3 v1], det [u1 u2/ v1 v2])

    For any vectors u,v,w in R3, w.(uxv)=D(w,u,v)

    Ax.y=x.A^Ty

    3. The attempt at a solution

    I'm not really sure how to find a standard matrix for this, so I haven't made much progress.
     
  2. jcsd
  3. Apr 3, 2012 #2

    Ray Vickson

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    If [itex]\textbf{y}= \textbf{a} \times \textbf{x}, [/itex] write [itex] y_1, y_2 \text{ and } y_3[/itex] in terms of [itex] x_1, x_2 \text{ and } x_3.[/itex]

    RGV
     
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