[PDF] determine if functions are linearly independent

16 nov. 2022 · Example 1 Determine if the following sets of functions are linearly dependent or linearly independent. f(x)  Questions associées
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  • How do you know if a function is linearly independent?

    One more definition: Two functions y 1 and y 2 are said to be linearly independent if neither function is a constant multiple of the other.
    For example, the functions y 1 = x 3 and y 2 = 5 x 3 are not linearly independent (they're linearly dependent), since y 2 is clearly a constant multiple of y 1.

  • How do you tell if a function is dependent or independent?

    Systems of equations can be classified by the number of solutions.
    If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent .
    If a consistent system has an infinite number of solutions, it is dependent .

  • How do you tell if a function is dependent or independent?

    A set of two vectors is linearly independent if and only if neither of the vectors is a multiple of the other.
    A set of vectors S = {v1,v2,,vp} in Rn containing the zero vector is linearly dependent.
    Theorem If a set contains more vectors than there are entries in each vector, then the set is linearly dependent.

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