1. The problem statement, all variables and given/known data Let M2 denote the set of all 2x2 matrices. We define addition with the standard addition of matrices, but with scalar multiplication given by: k [itex]\otimes[/itex] [a b c d] = [ka b c kd] (note that they are matrices) Where k is a scalar. Which of the following fails to hold? a. m2 is closed under scalar multiplication b. (ks)matrix = k [itex]\otimes[/itex] ( s [itex]\otimes[/itex] (matrix) c. 1 [itex]\otimes[/itex] (matrix) = (matrix) d. k [itex]\otimes[/itex](matrix + matrix') = k (matrix) + k (matrix') [Too lazy to inpute the otimes] e. (k+s) (matrix) = k(matrix) + s(matrix) 2. Relevant equations 3. The attempt at a solution I think the answer is E because if you multiply k+s to the matrix first then you can't split them.