A 3x3 symmetric matrix has a null space of dimension one containing the vector (1,1,1). Find bases and dimensions of the column space, row space, and left null space.
I know that, since the matrix is 3x3 and the dimension of the null space is one, the dimension of the column space would be 2. I also know that since the matrix is symmetric, the left null space would be the same as the column space. But I'm having trouble figuring out how to find a basis without having the actual matrix.