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2. (25 pts) Consider the following matrix and its reduced row echelon form: 12 1 -11 1 -6 -3 -12 A = OOHO OOVO NONO

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2. (25 pts) Consider the following matrix and its reduced row echelon form: 12 1 -11 1 -6 -3 -12 A = OOHO OOVO NONO OHOO OOOH 2 12 1 11 rref ( A) = 6 2 (a) What is rank(A)? (b) Without finding the subspaces, what are dim(null(A) ) and dim(im(A) )? Explain your answer. (c) Find null(A), im(A), and row (A)

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