The Relationship Between Nonzero Vectors And Scalars In Math: Proving K=0 When Ku=0 And U Is Nonzero

If u is a vector and k is a scalar such that ku = 0, then it must be true that k = 0.

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If u is a nonzero vector and k is a scalar such that ku = 0, then it must be true that k = 0.

To see why this is true, suppose that u is a nonzero vector, and that ku = 0 for some scalar k. Then either k is zero, or u is a zero vector. But if u is nonzero, then it cannot be the zero vector, so we must have k = 0.

To put it another way, if k is nonzero, then ku is a nonzero scalar multiple of u, which means that ku cannot be equal to zero unless u is the zero vector. Therefore, if ku = 0 and u is nonzero, then k must be zero.

So the statement is true: if u is a nonzero vector and k is a scalar such that ku=0, then it must be true that k=0.

More Answers:
Vector Spaces: Why Functions Passing Through The Origin Are Not Necessarily Zero Vectors In F (-Infinity, Infinity)
Vector Equivalence: Exploring (-1)U And -U In Vector Spaces
Is The Set Of Positive Real Numbers A Vector Space? An In-Depth Analysis

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