Reference no: EM132587002

Question:

(a) Show that R² is an inner product space under the following definition of inner product.

(b) Let v^→ = (v₁, v₂, v₃) and u^→ = (u₁, u₂, u₃)and define an operation <u, v> = u₁v₁ + u₂ + u₃v₃

Determine if this operation is an inner product on R³, and if not state which condition fail.

(c) The trace of a square matrix A is denoted by tr (A) and it is defined to be the sum of the entries on their main diagonal of A. Let A and B be elements of M_n(R). Show that <A, B> = tr(AB^T) defines an inner product on M_n(R).