2. Define two ordered bases B = and E = on R³. (i) Find the vector vị of R³ whose component vector with respect to B is [V1]B = 2 and write its component vector [V1]E with respect to E. (ii) Find the 3 × 3 change-of-basis matrix PE-B. Check your answer by computing [vi]E = PE-B[Vi]B, and comparing to what you found in part (i). (iii) Invert PE-B to find PBE. Then use PBte to find the component vector [v2]B of V2 relative to B.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.