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Please explain linear dependence and explain what is meant by vectors being linearly independent

Please explain linear dependence and explain what is meant by vectors being linearly independent

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Answer #1

a1, a2, a3,...are a set of Linearly Independent vectors if no vector in the set can be written as a linear combination of other vectors.

IF

Then, for Linear Independence

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a1, a2, a3,...are a set of Linearly Independent vectors if atleast one vector in the set can be written as a linear combination of other vectors.

IF

Then, for Linearly dependent vectors atleast one of the constants is non-zero. Suppose c1 is non-zero implies

Hence, a1 is expressed as a linear combination of other vectors and a1, a2, a3.... are Linearly Dependent

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