MATH 221 Midterm: MATH 221 2005 Winter Test 2

??-2 Assignment 3 0 3-4 51 8. For the matrix A-2 22 02 18 4 -6 a) Find a basis for the row space of A b) Find a basis for the column space of A 1 What is the rank of A? d) Find the nullspace of A and give the nullity of A

14) Suppose that the vectors Vi = (-2, 1, 0, 0, 0), ½ = (-4,0,-3,-2, 1) are a basis for nullspace of a 4X5 matrix A. Find a vector X such that X 0, ? , ? ½ and AX 0.

Determine whether b is in the column space of A. A = [1 1 -3 2 4 -2 -3 -6 5], b = [1 -2 -3] No Yes Find a basis for the null space of the matrix. A = [1 0 0 0 1 0 -7 5 0 -4 -2 0 {[7 -5 1 0], [4 2 0 1]} {[1 0 0], [0 1 0]} {[-7 5 1 0], [-4 -2 0 1]} {[1 0 -7 -4], [0 1 5 -2]}