Chapter 4 - Vector Spaces - 4.6 Exercises - Page 239: 7

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Given a 4 x 7 matrix A with four pivot columns. a) The number of pivot columns defines the rank of the Matrix, therefore the rank of the matrix is 4 and hence it spans $R^4$ - Statement is true. b) by the Rank theorem; $dim\,NulA=n-Rank A$ $n=7$ $Rank A=4$ $dim\,NulA=7-4=3$ Dimension of Nul A is 3 in a subspace of $R^7$ The statement is false