A is an arbitrary mxn matrix. B is a square nxn matrix C is a nonsingular square nxn matrix. R(A) = Col (A) is the "range", or column space of A.
True False. Rank (A) £ n and Rank (A) £ m.
True False. Rank (B) = Rank (C) = n.
True False. R(A) is a subspace of Rm
True False. The columns of A are a basis of R(A).
True False. If the columns of B are linearly independent, then so are the rows of B.
True False. Rank (AT ) = Rank (A).
True False. The dimensions of the row space and the column space of A are equal.
True False. If the nullity of B is 1, then the rank of B is n+1.
True False. R(C) = Rn.
True False. If A is row equivalent to B, then m = n, and they have the same row space.
Written by S.Hudson
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