(Solved): 5 Find the matrix of the quadratic form. Assume \( \mathrm{x} \) is in \( \mathrm{R}^{3} \). a. \( 6 ...

Find the matrix of the quadratic form. Assume \( \mathrm{x} \) is in \( \mathrm{R}^{3} \). a. \( 6 x_{1}^{2}-8 x_{2}^{2}+5 x_{3}^{2}+18 x_{1} x_{2}-16 x_{1} x_{3} \) b. \( 5 x_{3}^{2}-6 x_{1} x_{2}+8 x_{2} x_{3} \) a. The matrix of the quadratic form \( 6 x_{1}^{2}-8 x_{2}^{2}+5 x_{3}^{2}+18 x_{1} x_{2}-16 x_{1} x_{3} \) is (Simplify your answer.) b. The matrix of the quadratic form \( 5 x_{3}^{2}-6 x_{1} x_{2}+8 x_{2} x_{3} \) is (Simplify your answer.)