Answer to Question #46094 in Other Engineering for Sapna

Question #46094
a) Let a quadratic form have the expression x 2 + y 2 + 2z 2 + 2xy + 3xz with respect to the standard basis B 1 = f(1; 0; 0); (0; 1; 0); (0; 0; 1)g. Find its expression with respect to the basis B 2 = f(1; 1; 1); (0; 1; 0); (0; 1; 1)g (3) b) Consider the quadratic form Q : 2x 2 4xy + y 2 + 4xz + 3z 2 i) Find a symmetric matrix A such that Q = X t AX . ii) Find the orthogonal canonical reduction of the quadratic form. iii) Find the principal axes of the form. iv) Find the rank and signature of the form. (5)
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