Question: Let K be a positive definite 3 3 matrix. (a) Prove that the quadratic equation xTKx = 1 defines an ellipsoid in R3. What

Let K be a positive definite 3 × 3 matrix.
(a) Prove that the quadratic equation xTKx = 1 defines an ellipsoid in R3. What are its principal axes and semi-axes?
(b) Describe the surface defined by the quadratic equation 11x2 - 8xy + 20y2 - 10xz + 8yz + 11z2 = 1.

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