Question

Consider the homogeneous linear system 45+y+3 z=0,22 +2y=0,-1-3=0] Give the coefficient matrix for this system: ab sina a az f Give the augmented matrix for this system: ab sin(a) :: 8 a 2 Reduce the augmented matrix to reduced row-echelon form: b sin (@ a ar ::: Give a basis for the set of all solutions of the system. Syntax: Enter your answer as a set of vectors in one of the following forms (depending on the number of vectors in your basis): 0 {< 41, U2, 3 >> {< 41, 42, 43 ><V1, V2, uz >} {< 41:42, u3 >><01,02,03 >,<21:42,u3 >}

Answer 1

Consider the given homogeneous linear system 48+4+3.2=0 2x+ry -o - X-ZO * The coefficient matrix for this system is 1 3 2 2 -1 -1 * The Augmented matrise for this (Alo] system is u 1 3 2 2 1 * The reduced row echelon form of augmented meetrise is CATO . 0 1 -1 at from second row x3 is free variable and X2=3 from first yow we have - Thus X=-23 set x2 x3 1-01-18 23 23 thas basis for the set of all solutions of the is R={<-2, ;1}} system