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1.7 Linear Independence. in R n is said to be linearly independent if has only the trivial solution. in R n is said to be linearly dependent if there.

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Presentation on theme: "1.7 Linear Independence. in R n is said to be linearly independent if has only the trivial solution. in R n is said to be linearly dependent if there."— Presentation transcript:

1 1.7 Linear Independence

2 in R n is said to be linearly independent if has only the trivial solution. in R n is said to be linearly dependent if there exist weights, not all zero, such that Definitions

3 Examples: Determine if each of the following sets of vectors are linearly independent.

4 The columns of a matrix A are linearly independent if and only if has only the trivial solution. Examples: Determine if the columns of the following matrices are linearly independent.

5 Tips to determine the linear dependence 1.The set has two vectors and one is a multiple of the other. 2. The set has two or more vectors and one of the vectors is a linear combination of the others. 3. The set contains more vectors than the number of entries in each vector. 4.The set contains the zero vector. A set of vectors are linearly dependent if any of the following are true:

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