5 . Let A = [ 1 − 1 2 3 2 − 2 5 4 1 − 1 0 7 ] a ) Reduce the matrix A to echelon form, and determine the rank and nullity of A . b ) Exhibit a basis for the row space of A . c ) Find a basis for the column space of A (that is, for R ( A ) ) consisting of columns of A . d ) Use the answers obtained in parts b ) and c ) to exhibit bases for the row space and the column space of A T . e ) Find the basis for N ( A ) .
5 . Let A = [ 1 − 1 2 3 2 − 2 5 4 1 − 1 0 7 ] a ) Reduce the matrix A to echelon form, and determine the rank and nullity of A . b ) Exhibit a basis for the row space of A . c ) Find a basis for the column space of A (that is, for R ( A ) ) consisting of columns of A . d ) Use the answers obtained in parts b ) and c ) to exhibit bases for the row space and the column space of A T . e ) Find the basis for N ( A ) .
Solution Summary: The author explains the reduction of matrix A to echelon form and the rank and nullity of the matrix.
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