Let xTAx be a quadratic form in x1, x2,..., xn and define T: Rn R by

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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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Elementary Linear Algebra with Applications

ISBN: 978-0471669593

9th edition

Authors: Howard Anton, Chris Rorres

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Question Posted: Jun 17, 2016 08:14 AM

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Let xTAx be a quadratic form in x1, x2,..., xn and define T: Rn R by

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a By definition Tx y x y T Ax y x T y T Ax y x T Ax x T Ay y T Ax y T A y Tx x T A...View the full answer

Elementary Linear Algebra with Applications

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