Let B the the standard ordered basis on M2x2 (R), let y = {1, x}, and let T : M2x2 (R) → P1 (R) be the linear transformation such that 1 2 1 -4 :) -1 [T]; 3 Given that 2 1 T -1 -1 1 = a + bx, find the value of the number a.

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.