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1 The vector V1 = -8 spans a subspace V of the indicated Euclidean space. Find a basis for the orthogonal complement v of V. 4 Select the correct choice below and, if necessary, fill in the answer box within your choice. OA Evt A basis for the orthogonal complement is { {} (Use a comma to separate vectors as needed.) There is no basis for the orthogonal complement v. OB.
#8 6.4.8 Question Help 1 The vectors v1 1 -2 and V2 form an The orthonormal basis of the subspace spanned by the vectors is O. (Use a comma to separate vectors as needed.) 5 3 orthogonal basis for W. Find an orthonormal basis for W.
Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in span(V1, V2, V3) such that (V1, V1) = 51, (V2, V2) = 638, (V3, V3) = 36, (w, V1) = 153, (w, v2) = 4466, (w, V3) = -36, then W = _______ V1 + _______ V2+ _______ V3.
(1 point) Are the following statements true or false? ? 1. If W = Span{V1, V2, V3 }, and if {V1, V2, V3 } is an orthogonal set in W, then {V1, V2, V3 } is an orthonormal basis for W. ? 2. If x is not in a subspace W, projw(x) is not zero. then x ? 3. In a QR factorization, say A = QR (when A has linearly independent columns), the columns of Q form an orthonormal...
חו (1 point) Suppose V1, V2, V3 is an orthogonal set of vectors in R Let w be a vector in span(V1, V2, V3) such that (v1,vi) = 24, (v2,v2) = 21, (V3, V3) = 9, (w,v) 120, (w, v2) = 147, (w,v3) -36, Vi+ V2+ then w= V3.
Find an orthogonal basis for the column space of the matrix to the right. -1 5 5 1 -7 4 1 - 1 7 1 -3 -4 An orthogonal basis for the column space of the given matrix is O. (Type a vector or list of vectors. Use a comma to separate vectors as needed.) The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for 3 W. 6 -2 An...
Question 1 (10 points) Projection matrix and Normal equation: Consider the vectors v1 = (1, 2, 1), V2 = (2,4, 2), V3 = (0,1,0), and v4 = (3, 7,3). (a) (2 points) Obtain a basis for R3 that includes as many of these vectors as possible. (b) (4 points) Obtain the orthogonal projection matrices onto the plane V = span{v1, v3} and its perpendicular complement V+. (c) (2 points) Use this result to decompose the vector b= (-1,1,1) into a...
7. Let W = Span{x1, x2}, where x1 = [1 2 4]" and X2 – [5 5 5]" a. (4 pts) Construct an orthogonal basis {V1, V2} for W. b. (4 pts) Compute the orthogonal projection of y = [0 1]' onto W. C. (2 pts) Write a vector V3 such that {V1, V2, V3} is an orthogonal basis for R", where vi and v2 are the vectors computed in (a).
(1 point) Suppose V1, V2, U3 is an orthogonal set of vectors in R. Let w be a vector in Span(V1, U2, U3) such that 01.01 = 33, U2 · U2 = 10.25, 03 · 03 = 36, W • V1 = 99, w · U2 = 71.75, w · Uz = -108, then w = Vi+ U2+ U3
4 4. Here are two vectors in R". Let V - the span of fv,v,). a. Find an orthogonal basis for V (the orthogonal complement of V). You get an extra point for expressing your basis as vectors with integer components. b. Find a vector that is neither completely in V, nor completely in c. Find a vector in V which is a unit vector.