6. Determine whether the following linear transformations are one-to-one. Are they onto? Justify your answer. (a) Sı : M2(R) → R defined by S1(A) = a11 + a22. (b) S2 : M2(R) → M2(R) defined by S2(A) = A+ A". (c) S3 : Po(R) → P; (R) (t)dt. defined by S3(p(x)) = | p

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.