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Math Help - Finding out if a polynomial corresponds to a linar transformaion

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    Finding out if a polynomial corresponds to a linar transformaion

    I'm not sure what this problem is asking me to do:

    Consider the operation M:P2 -> P3 that takes p(x) in P2 to xp(x) in P3. Does this correspond to a linear transformation from R^3 to R^4? if so, what is its matrix?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Sherina View Post
    I'm not sure what this problem is asking me to do:

    Consider the operation M:P2 -> P3 that takes p(x) in P2 to xp(x) in P3. Does this correspond to a linear transformation from R^3 to R^4? if so, what is its matrix?
    It's asking you for this. We know that for P_2 there is a natural isomorphism \phi between P_2 and \mathbb{R}^3 by a_0+a_1x+a_2x^2\mapsto (a_0,a_1,a_2) and a similar one, call it \varphi, between P_3 and \mathbb{R}^4. If M were a linear transformation then so would \varphi^{-1}\circ M\circ \phi:\mathbb{R}^3\to\mathbb{R}^4. So, is M a linear transformation?
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