Homework SourseLet w Span 1 2 1 and x 1 4 9 What is the distance from x t
Let w = Span {[1 -2 1]} and x = [1 -4 9]. What is the distance from x to W? a) Squareroot 68 b) Squareroot 24 c) Squareroot 96 d) Squareroot 44![Let w = Span {[1 -2 1]} and x = [1 -4 9]. What is the distance from x to W? a) Squareroot 68 b) Squareroot 24 c) Squareroot 96 d) Squareroot 44SolutionLet v =(](/WebImages/41/let-w-span-1-2-1-and-x-1-4-9-what-is-the-distance-from-x-t-1128215-1761602089-0.webp "Let w = Span {[1 -2 1]} and x = [1 -4 9]. What is the distance from x to W? a) Squareroot 68 b) Squareroot 24 c) Squareroot 96 d) Squareroot 44SolutionLet v =(")
Solution
Let v =( 1,-2,1)T.The projection of x onto W is Projv (x) = [(1,-4,9)T.(1,-2,1)T/(1,-2,1)T.(1,-2,1)T ](1,-2,1)T = [(1+8+9)/(1+4+1)] (1,-2,1)T = (18/6)(1,-2,1)T = 3(1,-2,1)T = (3, -6, 3)T = u (say). Now, since u is perpendicular to W, the distance from x to W is ||u|| ={ (3)2 +(-6)2+(3)2} = ( 9+36+9) = 54
