Symmetric Matrices Consider the quadratic form Q(x) 9x 7x 11 x 8x,x2 8x1x3 Write the symmetric matrix A associated to the quadratic form Q 2 marks b Compute the determinant of A 3 marks a Let 1 12 s 13 be the eigenvalues of the matrix A We have 1, 13 15 3 and 12 9, and 3D 3D We have v2 1 2 2 is an eigenvector of A corresponding to 12 v3 2 1 2 is an eigenvector of A corresponding to 13 and c Compute the eigenvector v, of A corresponding to 24 3 marks d Compute an orthogonal matrix P such that the change of variable x Py transform x' Ax into a quadratic form with no cross product term 4 marks (Hint orthonormalize the eigenvectors) e Write the new quadratic form 2 marks MacBook Pro

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Question: Symmetric Matrices Consider the quadratic form Q(x) = 9x? + 7x + 11 x 8x,x2 + 8x1x3 Write the symmetric matrix A associated to

Symmetric Matrices Consider the quadratic form Q(x) = 9x? + 7x +

Symmetric Matrices Consider the quadratic form Q(x) = 9x? + 7x + 11 x 8x,x2 + 8x1x3 Write the symmetric matrix A associated to the quadratic form Q. [2 marks] b. Compute the determinant of A. [3 marks] a. Let 1

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