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3. Consider the quadratic form q(x1, X2, X3) := X7 + x3 + 2x1x2 - 4x1X3 + 2x2x3, (X1, X2, X3) ER3. (a) Find the

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3. Consider the quadratic form q(x1, X2, X3) := X7 + x3 + 2x1x2 - 4x1X3 + 2x2x3, (X1, X2, X3) ER3. (a) Find the symmetric matrix A representing q. (b) Find a corresponding orthogonal matrix P of eigenvectors of A. (c) Write down the maximum and minimum values taken by q over the unit vectors in R3

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