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Math Help - matrix of a linear transformation

  1. #1
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    matrix of a linear transformation

    Consider the polynomials f(t) = t + 1 and g(t) = (t + 2)(t + k), where k is an arbitrary constant. For which values of the constant k are the three polynomials f(t), tf(t) and g(t) a basis of P2?
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    This will happen when the matrix of coefficients

    \left(<br />
\begin{array}{lll}<br />
 1 & 0 & 2 k \\<br />
 1 & 1 & k+2 \\<br />
 0 & 1 & 1<br />
\end{array}<br />
\right)

    is nonsingular. Evaluate its determinant, and find the values of k for which it is nonzero.
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