Recent content by vellum93

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    Finding x for a certain quadratic form

    I think I've solved it. It involves setting up the equation q( x1 x2 x3) = [x1 x2 x3] * A * (x1 x2)
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    Finding x for a certain quadratic form

    Homework Statement Suppose a,c>0 and b^2-4ac>0 . Explain how you could find x_1, x_2 ε ℝ such that a(x_1) ^2+bx_1x_2+c(x_2)^2<0 . Homework Equations q\begin{pmatrix}x_1\\x_2\end{pmatrix} = a(x_1)^2+bx_1x_2+c(x_2)^2 The Attempt at a Solution I'm not sure where to go with this...
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    Finding a matrix, given one eigenvalue

    The other eigenvalue is the same isn't it? So there's only one distinct eigenvalue? For the matrix B^3, I put the eigenvalues on the diagonal and then 0's in the other two spots.
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    Finding a matrix, given one eigenvalue

    Ok, thanks for the help everyone. Does this mean then that B^3 has eigenvalues that are equal to -3√3? I just cubed the eigenvalues for B after factoring out a √3.
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    Finding a matrix, given one eigenvalue

    Homework Statement Suppose B is a real 2x2 matrix with the following eigenvalue: \frac{√3}{2} + \frac{3i}{2}. Find B^3. Homework Equations One of the hints is to consider diagonalization over C together with the fact that (\frac{1}{2} + \frac{√3}{2}i)^3 = -1. The Attempt...