Let A be the matrix of the quadratic form 9x + 7x + 11xỷ – 8x1x2 + 8x1.x3 It can be shown that the eigenvalues of A are 3, 9, and 15. Find an orthogonal matrix P such that the change of variable x = Py transforms x'Ax into a quadratic form with no cross- product term. Give P and the new quadratic form.

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Q: Let A be the matrix of the quadratic form 9x} + 7x3 + 11x – 8x1x2 + 8x1x3 It can be shown that the…

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A: Given that A=-1203Now, the characterstics equation is |A-λI |=0⇒-1-λ203-λ=0⇒(-1-λ)(3-λ) =0⇒-1-λ =0…

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Q: 17. Let A be the 3 x 3 matrix for the quadratic form 9(x,)? + 7(x2)² + 11(x3)² – 8x,x2 + 8x1X3. It…

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A: Introduction :