a) Find the rank of A and a basis for the row space of A. b) Find the dimension and a basis for the zero space of A.

R is the reduced row echelon form of Q. Find a basis {b₁,b2, ..., bn} for the null space of Q. b₁ = b₂ Fill in vectors in numerical order. Leave blank those that are not needed. = b3 b4 = b5 = 6565 7070 -704 -306 4480 -1573 1694 168 74 - 1073 1579 2314 2492 -248 -108 8138 8764 872 -380 5553 -2613 3317 - 794 1169; R = 4111 -2814 280 122 -1783 - 1320 = 1 0 13 00 1 00 0 0 0 0 0 0 0 2 13 1 0 0 0 8 13 8 0 0 0 10 | 5 13 8 0 0

answer a b c

Find bases for the column space, the row space, and the null space of the matrix 1 3 1 1 3 11 6 4 16 0 10 You should verify that the Rank-Nullity Theorem holds. A = Basis for the column space of A Basis for the row space of A Basis for the null space of A { 1}