12. Reduce the Quadratic form \( Q(x, y, z)=3 x^{2}+3 z^{2}+4 x y+8 x z+8 y z \) into canonical form using linear transformation.
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Step 1: Write the matrix of the quadratic form The given quadratic form Q(x, y, z) can be written in matrix form as: Q(x, y, z) = (x, y, z) * A * (x, y, z)^T where A is a symmetric matrix: A = | 3 2 4 | | 2 0 4 | | 4 4 3 | Show more…
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