Consider the bases: B = {(7, -8, 2), (-3, 4, -1), (-3, 4, 0)}, B' = {(3, 2, 6), (1, 1, 3), (2, 2, 7)}, and the vector [x]g' (a) Find the transition matrix from B to B'. (b) Find the transition matrix from B' to B. (c) Find the coordinate matrix [x]B given the coordinate matrix [x]g'.

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.