Question

Linear Algebra

2) General Inner Products, Length, Distance and Angle a) Determine if (u,v)-3uiv,-u,v, is a dot product b) Show that (u.v)-a+a,h,'2 is a product if a, 20 e)Let A-(41 ..)and B-G ) Use inner product on 4 -2 M (A, B aitai +apb +2a to find the length of A, B, namely ll-41 and 1 d) Find the angle between the two matrices above e) Find the distance between the two above matrices 0) For the functions (x)-1 and g)3x1 with the inner product (f.g)-s(c)dr Find the norm of f and g, then the angle between f, g and the distance between f,g g) Repeat the above problem but use the Standard Inner Product on P h) Find the angle between vectors (-4,3) and (0,5) with respect to the product i) Show that f(x)-sinr and g(x)-cosx are orthogonal with respect to the inner product (f.g)-fr

Answer 1