I am taking a Linear Algebra course and have been stumped on a homework question for a few hours. How do I prove for two scalars, $c_1$ and $c_2$, and a vector $v$:
$(c_1 + v)c_2 \neq c_1c_2 + c_2v$
I am inexperienced at mathematical proofs. However, I know I cannot prove this by an example. I have attempted to apply the rules of scalar multiplication (e.g., additivity, compatible, commutativity, etc.), including that scalar multiplication is an external binary operation ($A \times B \to B$).
Any help that points me in the right direction would be greatly appreciated, along with any advice on how to improve this question (this is my first question on Math Stack Exchange.)
Thank you, Chris
One way to prove that is to notice that the expressions on both sides do not make sense.
For the left side, $c1$ is a scalar, while $\overrightarrow v$ is a vector, and adding a scalar and a vector is undefined (in standard vector space theory).
For the right side, $c1 \cdot c2$ is a scalar, while $c2 \cdot \overrightarrow v$ is a vector, and again the sum is undefined.