Solving systems of linear equations linear combinations quizlet

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  1. Math
  2. Algebra
  3. Linear Algebra

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Terms in this set (6)

(a) The zero vector is a linear combination of any nonempty set of vectors.

True

(b) The span of ∅ is ∅.

False

(c) If S is a subset of a vector space V, then span(S) equals the intersection of all subspaces of V that contain S.

True

(d) In solving a system of linear equations, it is permissible to multiply an equation by any constant.

False

(e) In solving a system of linear equations, it is permissible to add any multiple of one equation to another.

True

(f) Every system of linear equations has a solution.

False

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