1. For the following quadratic forms (i) write down the symmetric matrix A (so the form is equal to x"Ax), (ii) find matrices P, orthonormal, and D so that D diagonal, (iii) write the quadratic form in terms of y1,..., Yn where x = decide whether the form is positive/negative definite/semidefinite or indefinite. (a) 2x – 2x1x2 + 2x3 (b) –xỉ + 4x1x2 – 4x3 (c) 3x? + 4.x3 + 5xž + 4x1x2 – 4x2X3 (it may help to show that A characteristic polynomial of A). РТ АР is Py and (iv) 1 is a root of the %3D

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