I am extremely confused when it comes to linearly transformations and am not sure I entirely understand the concept. I have the following assignment question: Consider the 2x3 matrix A= 1 1 1 0 1 1 as a linear transformation from R3 to R2. a) Determine whether A is a injective (one-to-one) function. b) Determine whether A is a surjective (onto) function. For a) I said that we need to solve Ax=0 and the matrix then looks like: 1 1 1 : 0 0 1 1 : 0 Since x3 is a free variable A cannot be injective. For b) I have the matrix: 1 1 1 : * 0 1 1 : * (note that it doesn't matter what * is) This matrix is consistent so the matrix A is surjective. Am I understanding this question correctly?