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What does it mean if a vector is described as a linear combination of other vectors?
A. The vector can be expressed as the sum of the other vectors, each multiplied by a scalar coefficient.
B. The vector is orthogonal to the other vectors.
C. The vector has the same magnitude as the other vectors.
D. The vector is perpendicular to the plane defined by the other vectors.



Answer :

macaroni31

Answer:

If a vector is a linear combination of other vectors, it A. can be expressed as a sum of other vectors, each multiplied by a scalar coefficient.

Explanation:

A linear combination of vectors is a combination of vectors that have been scaled and added. If you have vectors v₁, v₂, ... vₙ in a subspace, and scalars c₁, c₂, ... cₙ, then a linear combination of these vectors can be represented by -

v = c₁v₁ + c₂v₂ + ... + cₙvₙ

Linear combinations can be used to decompose a vector, solve systems of linear equations, and much more.

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