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0 3 (1 point) Find the orthogonal projection of v= -18 -14 | onto the subspace V of R³ spanned by -2.. 4 and 2. 1 projv(v) =

Answer 1

Question Find the orthogonal projection v of subspace onto the Va 1-18 -14 -2 and -4 4 Rs spanned by 2 To find: pooj v () = ? the a solutions V let supspace spanned by u , & U. given vectors definition, the orthogonal projection of the By is ; V V onto penyys - ()" + ( ) have: we u, = & U₂= [:] V= 13] "[?] 18 -14 - 2 Now, [-4 4 2 (-4)² + (4)² + (2) ² U. U = 16+16+4 4.Un = 361

U..v= (-4 [-4 4 2 -18 = (-4) (-18) + (4) (-14) + (2)(-2) E -14 -2 = 72 - 56 - 4 U,. V = 12 2 (0)* + (0)2 +-1) 42:42 = [o 1 -1] - "" [3] M₂.42=2 -1] (c)(-18) +(1)(-14) + (-1) (-2) U₂.V=[0 -18 -14 - 2 0-14+2 U.V = M₂.v=-12 Thus, prej yo = 3:) + (22)[:) **]+[* - prog (u) -4/3 -14/3 20/3 Answer...