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12 marks a 6 marks Given the matrices A and the reduced echelon form of...

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Algebra

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12 marks a 6 marks Given the matrices A and the reduced echelon form of A below find i a basis for Row A What is the dimension of Row A ii a basis for Col A What is the dimension of Col A iii a basis for Nul A What is the dimension of Nul A A 1 23 4 5 10 1 2 1 2246 4 1 1 20 1 b 2 marks Consider vectors rref A 1 0 1 0 5 3 1 1 0 8 3 0 0 0 0 1 1 3 0 000 0 V 1 1 5 2 V2 2 3 1 0 V3 9 10 34 14 V4 0 4 2 3 v5 3 31 41 87 in R4 Find a basis and the dimension of the subspace W span V V2 V3 V4 V5 1 0 7 05 01 1 0 4 00 016 00 000 NOTE RREF of the matrix whose columns are vectors V V2 V3 V4 V5 is c 4 marks Let A be an m x n matrix Prove that every vector in the null space of A is orthogonal to every vector in the row space of A

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