Question: Let xTAx be a quadratic form in x1, x2,..., xn and define T: Rn R by T(x) = xTAx. (a) Show that T(x +

Let xTAx be a quadratic form in x1, x2,..., xn and define T: Rn → R by T(x) = xTAx.
(a) Show that T(x + y) = T(x) + 2xTAy + T(y).
(b) Show that T = (kx) = k2T(x).
(c) Is T a linear transformation? Explain.

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