Question

[1 -1 0 0 -2 0] 1 4 -4 0 0 -8 0 (1 point) Let A = 10 0 -1 2 -3 3 . Find a basis for the row space of A, a basis for the column space of A, a basis for the null space 0 0 0 -3 0 -2 Lo 0 1 0 3 3] [1 -1 0 0 -2 01 0 0 1 0 3 0 of A, the rank of A, and the nullity of A. (Note that the reduced row echelon form of A is 0 0 0 1 0 0 .) 0 0 0 0 0 1 Lo 0 0 0 0 0 Row Space basis: Column Space basis: Null Space basis: Rank: Nullity: To enter a basis into WebWork, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is | 2,1l}, then you would enter [1,2,3],[1,1,1) into the answer blank. 311

Answer 1

ه - 0 0 -2 0 4 -4 o os o o o -1 2-3 3 لم o o lo 33 o Reduced o-2 o vow of A is l echelen form . - . Co Rowspace non zero rous in the reduced - basis for Rowspace is rowe Chelon form. (1,-1,0,0,20), (0,0,1,0,3,0). .: basis for rowspace of Ais (0,0,0,1,0,0), (0,0,0,0,0,17% (1,-1,0,0,2,0], [0,0,1,0,3,0), [0,0,0,1,0,0], [0,0,0,0,0, 1]

Columnsface from reduced rowechelon form it has a pivots 6th Columns are first, 3rd, uth and pivet columns. are clumns of H basis for Column space 3rd, 4th & 6t from origina matriu Woo .: basis for column space of Ais = (1,4,9,0,0], [oro, m, 0, 1], [0, 0, 2, -3,03, [0,0,3, -2,3) Mullipale: from reduced rowechelen form *-, -25 20 2y - x2 = free vrible Xgt free variable A2+2a5 l theo ~3x8 0 li 0 basis for wallspace of Ais crow on [1,1,0,0,0,0], [2,0, -3,011, 0] Rank: of A = 4 Number of non zero rows in the reduced rowechelen 15m ( rank = number of rank & A = 4 leading entries Nullity - nullity a diments dimension of wellspace - columns without lendingentriy Number of freemably .: Nullity = 2 allity: