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Intros
Lessons
  1. Null Space Overview:
  2. Definition of the Null space
    N(A)=N(A) = null space
    • A set of all vectors which satisfy the solution Ax=0Ax=0
    Definition of the Null space
  3. A vector u in the null space
    • Multiply matrix AA and vector uu
    Au=0Au=0 means uu is in the null space
  4. Finding a basis for the null space
    • Solve for Ax=0Ax=0
    • Write the general solution in parametric vector form
    • The vectors you see in parametric vector form are the basis of N(A)N(A).
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Examples
Lessons
  1. Showing that the null space of AA is a subspace
    Show that N(A)N(A) (null space of AA) is a subspace by verifying the 3 properties:
    1) The zero vector is in N(A)N(A)
    2) For each uu and vv in the set N(A)N(A), the sum of u+vu+v is in N(A)N(A) (closed under addition)
    3) For each uu in the set N(A)N(A), the vector cucu is in N(A)N(A). (closed under scalar multiplication)
    1. Verifying a vector is in the null space
      Is the vector is this matrix in null space in the null space of the matrix
      null space of this matrix
      1. Is the vector Verifying a vector is in the null space in the null space of the matrix
        null space of this matrix
        1. Finding a basis for the null space
          Find a basis for the null space of AA if:
          Finding a basis for the null space
          1. Find a basis for the null space of AA if:
            Finding a basis for the null space