UCSF 137 Lecture 11: UCSF 137 - Lecture 11

Consider the following Gauss-Jordan reduction: [-5 0 1 5 -4 -1 1 0 0]_ A rightarrow [-5 0 1 0 -4 0 1 0 0]_ E_1A rightarrow [0 0 1 0 -4 0 1 0 0]_ E_2E_1A rightarrow [1 0 0 0 -4 0 0 0 1]_ E_3E_2E_1A rightarrow [1 0 0 0 1 0 0 0 1]_ E_4E_3E_2E_1 A = I Find E_1 = [], E_2 = [], E_3 = [], E_4 = []. Write A as a product A = E_1^-1 E_2^-1 E_3^-1 E_4^-1 of elementary matrices: [-5 0 1 5 -4 -1 1 0 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]}