Part a

For the matrix a8 defined below, experiment to find a positive integer t so that Null[l[t]] is not just the zero vector. Then find a basis for the nullspace.

In[88]:=

  a8={{5,5,3},{-7,-7,-3},{5,5,3}};
  l[t_]:=a8-t IdentityMatrix[3]
  MatrixForm[a8]
  MatrixForm[l[t]]

  SetDelayed::write: 

     Tag List in {{1, 1, 0, 0}, <<1>>, {1, 0, 1, 0}}[t_]

       is Protected.

Out[88]=

  $Failed

Out[89]=

  5    5    3
  
  -7   -7   -3
  
  5    5    3

Out[90]=

  {{1, 1, 0, 0}, {0, 0, 1, 1}, {1, 0, 1, 0}}[t]

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