Answer and Step-by-step explanation:
Proof: multiplicative property of scalar zero states that the product of any number and zero is zero.
So, 0 v= 0,
Let y be a field. We will denote one by an identity element and (-v) as an additive inverse of v.
0v = 0v + 0
=0v + (v + (-v)) by inverse element
= (0v + v) + (-v) by associative property of vector addition
= (0v + 1v) + (-v) by identity element of scalar multiplication
= (0 + 1) v + (-v) by distributive property of scalar multiplication
= (1v) + (-v) by identity element of scalar multiplication
= v + (-v) by inverse element of vector addition
=0
Hence proved.
