Show that if u is a vector in R^{2} or R&3, then u+(−1)u=0 u+(−1)u=0

amanf 2021-01-28 Answered
Show that if u is a vector in R^{2} or R&3, then u+(1)u=0
u+(1)u=0
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Expert Answer

Nathanael Webber
Answered 2021-01-29 Author has 117 answers

First, we will show that 0⋅u=0 for any vector u∈R^{2} or R^{3}. Now ​
0×u+0×u=(0+0)×u=0×u0×u+0×u+(0×u)=0×u+(0u)0×u+[0×u+(0×u)]=0×u+(0u)0×u+0=00×u=0
Therefore ​
u+(1)×u=1×u+(1)×u=(1+(1))×u)=0×u=0.

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