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no calculator please 2. (12 pts) Given the matrix in a R R-E form: [1 0...

no calculator please

2. (12 pts) Given the matrix in a R R-E form: [1 0 0 0 3 -2 1 1 0 0 0 0 0 1 0 0 0 0 0 0 (a) (6 pts) Find rank(A) and nullity(
2. (12 pts) Given the matrix in a R R-E form: [1 0 0 0 3 -2 1 1 0 0 0 0 0 1 0 0 0 0 0 0 (a) (6 pts) Find rank(A) and nullity(A), and nullity(AT). (b) (2 pts) Find a basis for the row space of A. (c) (2 pts) Find a basis for the column space of A. (d) (2 pts) Find a basis for the null space of A.
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2. 0 3 2 O 0 O O O 14x6 a> from the above RR-E form 3 rank (A)= nullity (A) number of column pank(A) 6 - 3 = 3 0 T A o 0 3 -(6) Row space of A is generated by (1,0,0,0, 3,-2), (0,1,1,0, -2,1), (0,0,0,1,1,1) and (0,0,0, consider 4 (1,0,0,0,3, -2) + C{(1,0,0,0), (1,0,0,0), (0,1,0,0) basis for for the column space the set forms of A (0, 0, 1,0)) (d) for finding null space of. (hrl2 ,U3, U4, KS, ko = (-3K2+2 kg -K3+2 K2 - kg K3g - 4-k2 g K2 ,k) V (2 Z ll K, (2,-1,0,1,0,1) + Kg (-3,2,0, 1, 1,0) +63(

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