Below is a proof of Theorem 4.1.1 (b): For the zero vector ⃗0 in any vector...

Below is a proof of Theorem 4.1.1 (b): For the zero vector ⃗0 in any vector space V and k ∈ R, k⃗0 = ⃗0.

Justify for each of the eight steps why it is true.
1. k⃗0+k⃗0=k(⃗0+⃗0)
2. = k ⃗0
3. k⃗0 is in V
4. and therefore −(k⃗0) is in V .
5. It follows that (k⃗0 + k⃗0) + (−k⃗0) = (k⃗0) + (−k⃗0)
6. and thus k⃗0 + (k⃗0 + (−k⃗0)) = (k⃗0) + (−k⃗0).
7. We conclude that k⃗0 + ⃗0 = ⃗0
8. and so k⃗0 = ⃗0, as desired.

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Expert Solution

Colby Messinger answered 1 year ago

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