- #1
FinalStand
- 60
- 0
Homework Statement
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)
Homework Equations
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.