Final answer:
The column space of a matrix is found by reducing it to echelon form and the nullspace is found by solving the homogeneous equation Ax=0. Both require the actual matrix elements, which are not provided in the question.
Step-by-step explanation:
Finding Column Space and Nullspace
To find the column space of a matrix, we look at the linear combinations of the columns of the matrix. It is essentially the range of the matrix's corresponding linear transformation. This space is spanned by the matrix's columns where they act as vectors. In practice, we find the column space by reducing the matrix to its echelon form and identifying the pivot columns. Those columns in the original matrix form the basis for the column space.
The nullspace, also known as the kernel of a matrix, consists of all the vectors that when multiplied by the matrix result in the zero vector. To find the nullspace, we must solve the homogeneous equation Ax=0, where A is the given matrix and x is the vector. This is typically done by reducing the matrix to row echelon form and then applying back substitution to find the general solution which will be a set of vectors that define the nullspace.
The provided information about three-dimensional space and Cartesian axes is essential for understanding how vectors operate in space, but to solve for a specific matrix's column space and nullspace, we would require the actual matrix elements, which are not provided here.