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Definition of linear combination of vectors
Example of linear combination of vectors in R^2
Definition of weights in a linear combination of vectors
Example of writing a given vector in R^3 as a linear combination of given vectors

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Example of linear combination of vectors in R^2

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Example of writing a given vector in R^3 as a linear combination of given vectorsClose match
Linear combinationsClose match
Definition of linear combination of vectorsClose match
Example of a sum of vectors interpreted geometrically in R^2Close match
Determine if a particular vector is in the span of a set of vectors in R^3Close match
Example of vector-scalar multiplication in R^2Close match
Linear (in)dependenceClose match
Definition of weights in a linear combination of vectorsClose match
A vector can be written uniquely as a linear combination of vectors from independent subspaces.Close match
Definition of linearly independent set of vectors: if a linear combination is 0Close match
A linear system is equivalent to a vector equation.Close match
SpansClose match
Definition of linear dependence relation on a set of vectorsClose match
A linear transformation of a linear combination is the linear combination of the linear transformationClose match
Determine if a particular vector is in the span of a set of vectors in R^2Close match
Theorem: a set of vectors is linearly dependent if and only if one of the vectors can be written as a linear combination of the other vectorsClose match
Definition of linearly dependent set of vectors: one of the vectors can be written as a linear combination of the other vectorsClose match
Determine if a particular set of vectors in R^3 in linearly independentClose match
Example of a linear transformation on R^2: rotationClose match
Example of a linear transformation on R^2: projectionClose match

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