Suppose s is a six-dimensional subspace of nine-dimensional space r 9 .

(a) what are the possible dimensions of subspaces orthogonal to s?

(b) what are the possible dimensions of the orthogonal complement s j_ of s?

( c) what is the smallest possible size of a matrix a that has row space s?

(d) what is the smallest possible size of a matrix b that has nullspace s j_ ?

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