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Finding the formula of a projection in M2x2 (R)

  1. Aug 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Let T : M2x2(ℝ) → M2x2(ℝ) denote the projection on W along U.

    W={
    [a b]
    [c d] : a+b+c+d=0 }

    U= span{ I2 }

    Find the matrix representation of T with respect to the standard basis of M2x2(ℝ) and the formula for T.

    2. Relevant equations

    From my notes, I know W is the range of T and U is the kernel of T.

    M2x2(ℝ) = W [itex]\oplus[/itex] U (Direct sum)

    3. The attempt at a solution

    I am unsure how to proceed. Any thoughts?
     
  2. jcsd
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