Vector Arithmetic

Monday, July 30, 2018

9:11 AM

Uniqueness of Zero
There is one, and only one zero vector
Cancellation Property
If 𝑢,𝑣,𝑤∈𝑍 and 𝑢+𝑣=𝑢+𝑤, then 𝑣=𝑤
For all 𝑣∈𝕍, there exists only one 𝑤∈𝕍 where 𝑣+𝑤=0

Prove the Cancellation Property for any vector space V

Prove that 𝜆0=0 for all 𝜆∈𝑅, ﷐ℝ﷮3﷯

Lambda 0 = 0
0v = 0
(-1)v= -v
Lambdav=0, lambda =0 or v = 0
Lambda v = mu v, v neq 0, lambda = mu

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