MTH501 Assignment no 3 Spring 2012 Idea Solution

Question: 1                                                                                                                               Marks: 10

Find a standard basis vector that can be added to the set {v₁, v₂} to produce a basis for R³ where;

   v₁ = (-1, 2, 3), v₂ = (1, -2, -2)

Question: 2                                                                                                                               Marks: 10

Let B = {b₁, b₂} and C = {c₁, c₂} be the bases for R². Find the change-of-coordinates matrix from B to C, and change-of-coordinates matrix from C to B where;