Linear Algebra, geometric multiplicity I have a matrix and the question says I that I have an eigenvalue of 0.
 The question asks me to find the geometric multiplicity of that eigenvalue. I know the answer      is 4. I just don't understand how it is 4 since this matrix can be reduced to just one row of 1 1 1 1 1and the rest of the rows are 0's. Thanks in advance for your comments/
  1 1 1 1 1 
  1 1 1 1 1
  2 2 2 2 2
  2 2 2 2 2
  2 2 2 2 2


Well, precisely because you can reduce your matrix to that is that the geometric multiplicity of zero is four...
Think it this way: you're looking for the dimension of the solution subspace of the homogeneous linear system whose coefficients' matrix is your matrix, so getting only one
 non-zero row after reducing the matrix means you have $\;4\;$ degrees of freedom to choose your general solution vector...voila!
