Mathematics II - Old Questions

10. Let B = {b₁, b₂} and C = (c₁, c₂) be bases for a vector  V, and suppose b₁ = -c₁ + 4c₂ and b₂ = 5c₁ - 3c₂. Find the change of coordinate matrix for a vector space and find [x]_c for x = 5b₁ + 3b₂.