finding column and null spaces

basis for the kernel of A is

{c1, c2, c3} where they are the vectors that linearly combine to make the vector

dim ker A (# free columns) + dim im A (# leading columns)

nullity + rank = # of columns of A

a basis of im A is

the leading columns of A, or those that correspond to leading variables in rref(A)

finding a basis for the span of some vectors

put them as columns or rows of a matrix - the leading columns in A or the nonzero rows of rref(A) are a basis

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