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The set a₁ a₂ a₃ will span r³ unless h=

a. h = 1
b. h =0
c. h is not equal to 0
d. h< 0

User FilmJ
by
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1 Answer

6 votes

Final answer:

The set of vectors a₁, a₂, a₃ will span R³ unless h is zero, which would prevent the third vector from contributing an additional dimension to the spanned space.

Step-by-step explanation:

The question is concerned with the conditions under which the set of vectors a₁ a₂ a₃ will span R³, which is a concept in linear algebra related to the ability of a set of vectors to cover the entire three-dimensional space through linear combinations. For a set of vectors to span R³, they must be linearly independent and there must be three of them, as each vector adds a dimension to the space that can be reached. In this context, h seems to be a parameter associated with vector a₃.

If h is zero (option b), vector a₃ could become a zero vector or fail to provide an additional dimension, and thus the set would not span R³. In all other cases (option a, c, and d), assuming a₁ and a₂ are linearly independent and non-zero, the vectors should span R³ as a₃ would not be a zero vector and would add the necessary third dimension to the spanned space.

User ISHIDA
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8.0k points
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