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

[math_maj0r]

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

 

[mrbohn1]

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.

 

[math_maj0r]

thanks a lot!