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Suppose that A is a 9 × 12 matrix and that T(x) = Ax. If T...

Suppose that A is a 9 × 12 matrix and that T(x) = Ax. If T is onto, then what is the dimension of the null space of A?

Suppose that A is a 9 × 5 matrix and that B is an equivalent matrix in echelon form. If B has one pivot column, what is nullity(A)?

Suppose that A is an n × m matrix, with rank(A) = 3, nullity(A) = 4, and col(A) a subspace of R6. What are the dimensions of A? (n, m) =

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