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

Show that if u is a vector in R^{2} or R&3, then $u+\left(-1\right)u=0$
$u+\left(-1\right)u=0$
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Nathanael Webber

First, we will show that 0⋅u=0 for any vector u∈R^{2} or R^{3}. Now ​
$0×u+0×u=\left(0+0\right)×u=0×u⇒0×u+0×u+\left(-0×u\right)=0×u+\left(-0\cdot u\right)⇒0×u+\left[0×u+\left(-0×u\right)\right]=0×u+\left(-0\cdot u\right)⇒0×u+0=0⇒0×u=0$
Therefore ​
$u+\left(-1\right)×u=1×u+\left(-1\right)×u=\left(1+\left(-1\right)\right)×u\right)=0×u=0.$