Keyword Analysis & Research: linearly dependent and independent vectors

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How to determine if a vector set is linearly independent?

set of vectors is linearly independent: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero The set is of course dependent if the determinant is zero. Example The vectors <1,2> and <-5,3> are linearly independent since the matrix has a non-zero determinant. Example

What does it mean to be linearly independent?

The vectors a 1, ..., a n are called linearly independent if there are no non-trivial combination of these vectors equal to the zero vector. That is, the vector a 1 , ..., a n are linearly independent if x 1 a 1 + ... + x n a n = 0 if and only if x 1 = 0, ..., x n = 0.

Which are the independent and dependent variables?

The relationship of the dependent variable and each of the independent variables can be direct or inverse. In a direct relationship, a higher value of the independent variable is related to a higher value of the dependent variable (or vice-versa). Mathematically, a direct relationship is also a positive relationship.

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