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1MileCrash
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Homework Statement
Prove that a0 = 0
Homework Equations
The Attempt at a Solution
Let V be a vector space on a field F. Let x be a member of V and a be a member of F.
Consider that the 0 vector is the unique vector such that
x + 0 = x
Now, apply a scalar multiplication by a to both sides of the equation. Because scalar multiplication is distributive in all vector spaces,
ax + a0 = ax
Thus, we see that a0 has the same property of the 0 vector in V. Since the 0 vector in V is also unique, it must be the case that
a0 = 0
QEDCan I do that?