In real number multiplication, if uv 1 uv 2 and u 0, we can cancel the u and conclude that v 1 v 2 Does the same rule hold for the dot product That is, if u v 1 u v 2 and u 0, can you conclude that v 1 v 2 Give reasons for your answer ...

ANSWER The same rule does not hold for the dot product In fact we cannot ...

In real-number multiplication, if uv 1 = uv 2 and u 0, we can cancel the

Question:

In real-number multiplication, if uv₁ = uv₂ and u ≠ 0, we can cancel the u and conclude that v₁ = v₂ . Does the same rule hold for the dot product? That is, if u · v₁ = u · v₂ and u ≠ 0, can you conclude that v₁ = v₂? Give reasons for your answer.