Given f be a bilinear form in a 3D vector space V and the matrix for...

 

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Given f be a bilinear form in a 3D vector space V and the matrix for the base B = 1 -1 {U1, U2, U3} be A -2 -2 . Given h :V→V be a linear transformation whose the %3D 3 4 5 1 1 matrix corresponding with B is B= -3 -4 1 -2 -3 а) Compute f(и,;из);f(u, — иz+uз, 2u, + Зи2 — из) b) Show that the map g(u, v) = f (u, h(v)) is a bilinear form in V. Find the matrix of g corresponding with B. Given f be a bilinear form in a 3D vector space V and the matrix for the base B = 1 -1 {U1, U2, U3} be A -2 -2 . Given h :V→V be a linear transformation whose the %3D 3 4 5 1 1 matrix corresponding with B is B= -3 -4 1 -2 -3 а) Compute f(и,;из);f(u, — иz+uз, 2u, + Зи2 — из) b) Show that the map g(u, v) = f (u, h(v)) is a bilinear form in V. Find the matrix of g corresponding with B.

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