Problem 1 Suppose A, B, C, D, E are matrices with the following sizes A B с D E 4x5 4x5 5x2 4x2 5x4 Determine whether the given matrix expression is defined. For those that are defined, give the size of the resulting matrix. (1) B-A (2) A C+D (3) E. (A.C) (4) E. (5B+A) (5) D.C (6) B-C-3D

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.