The SOLUTION SET of a MATRIX is a point, line, plane or cube

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Main Question or Discussion Point

How do you know if the solution set of a matrix is a point, line, plane or cube? How do you know the dimension of the solution set?

P.S.: This is NOT a homework question. It's a general question about something I'm not 100% clear about
 

Answers and Replies

  • #2
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The dimension of the solution set is the dimension of the null-space. The dimension of the null-space (nullity) can be found by finding the rank of the matrix (use row and column operations to put the matrix in echelon form and count the number of non-zero rows), and subtracting this from the dimension of the matrix.
 
  • #3
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thanks a lot!
 

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