Linear independence

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Intros
Lessons
  1. Linear Independence Overview:
  2. Linearly independent
    • Definition of linear independence
    • Trivial solution
  3. Linearly dependent
    • Definition of linear dependence
    • Non-trivial solutions
  4. Fast ways to determine linear dependence
    • Vectors are multiples of one another
    • # of Vectors > # of Entries in each vector
    • Zero Matrix
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Examples
Lessons
  1. Determining Linear independence by solving
    Determine if the following vectors are linearly independent:
    is this vector linearly independent
    1. Determine if the matrix is linearly independent by solving Ax=0Ax=0:
      linearly independent matrix
      1. Determining Linear dependence by inspection
        Determine by inspection if the following vectors are linearly dependent:
        1. determine if vector is linearly dependent by inspection
        2. determine if vector is linearly dependent by inspection
        3. determine if vector is linearly dependent by inspection
        4. determine if vector is linearly dependent by inspection
      2. Linear dependence/independence with unknown constant
        Find the value(s) of kk for which the vectors are linearly dependent.
        find the unknown value if the vectors are linearly dependent