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Math Help - Can anybody help me?

  1. #1
    Newbie
    Joined
    Oct 2009
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    Red face Can anybody help me?

    I got two questions about proving linear mapping stuff. For questions number 5 and 6 in the attachment! ThanksMATH_136-Assign5-F09.pdf

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  2. #2
    Super Member
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    Apr 2009
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    México
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    Remember that a function f: \mathbb{R} ^n \rightarrow \mathbb{R}^m is linear iff for all x,y \in \mathbb{R} ^n and a,b \in \mathbb{R} we have f(ax+by)=af(x)+bf(y). If you have g,h: \mathbb{R} ^n \rightarrow \mathbb{R}^m the sum (g+h)(x):=g(x)+h(x) and (ag)(x):=ag(x). It should be clear from here, just try to work them out.

    For the second one suppose L: \mathbb{R} ^n \rightarrow \mathbb{R}^m and M: \mathbb{R} ^m \rightarrow \mathbb{R}^p are linear take x,y \in \mathbb{R} ^n and a,b \in \mathbb{R} then M \circ L(ax+by)=M(L(ax+by)=M(aL(x)+bL(y))=aM(L(x))+bM(L(y  ))
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