State if the following statement is true or false. The set of vectors B={u=(1,1,4)=(2,0,2);= (0,2,1)) is linearly independent in the vector space R³. ue Ise
What is Linear Independence:
A set of vectors is said to be linearly dependent in the theory of vector spaces if there is a nontrivial linear combination of the vectors that equals the zero vector. The vectors are considered to be linearly independent if there is no such linear combination. The definition of dimension is based on these ideas. The maximum number of linearly independent vectors determines whether a vector space has finite or infinite dimensions. Determining the dimension of a vector space depends critically on the definition of linear dependence and the capability to assess whether a subset of vectors in a vector space is linearly dependent.
Given:
Given set of vectors is,
.
To Determine:
Whether the set is linearly independent or not.
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