... Let v = , u = , and let W the subspace of R4 spanned by v and u. Find a basis of W .
(5 points) Let 5 -4 v= 1-3 -3 and let W the subspace of R4 spanned by ū and 7. Find a basis of W?, the orthogonal complement of W in R4.
(1 point) Let u = 1. VE L . and let W the subspace of R4 spanned by {u, v}. Find a basis for WI. Answer:
(1 point) Find the orthogonal projection of U = onto the subspace W of R4 spanned by --0-0-1 Uw =
Let W be the subspace of R4 spanned by the orthogonal vectors 1 0 0 ui , ua : 0 1 Find the orthogonal decomposition of v = ܝܬ ܥ 5 -4 6 with respect to W. -5 p= projw (v) = q= perpw («) =
Q6. Let W be the subspace of R' spanned by the vectors u. = 3(1, -1,1,1), uz = 5(–1,1,1,1). (a) Check that {uj,uz) is an orthonormal set using the dot product on R. (Hence it forms an orthonormal basis for W.) (b) Let w = (-1,1,5,5) EW. Using the formula in the box above, express was a linear combination of u and u. (c) Let v = (-1,1,3,5) = R'. Find the orthogonal projection of v onto W.
Problem #8: Find a basis for the orthogonal complement of the subspace of R4 spanned by the following vectors. v1 = (1,-1,4,7), v2 = (2,-1,3,6), v3 = (-1,2,-9, -15) The required basis can be written in the form {(x, y, 1,0), (2,w,0,1)}. Enter the values of x, y, z, and w (in that order) into the answer box below, separated with commas.
Let W be the subspace spanned by the given vectors. Find a basis for Wt, 0 1 A. W1 = W2 = 3 2 -1 2 B. W W2 2 -3 W3 = 6
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V) 0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)
Show that w is in the subspace of R4 spanned by vy. Vz, and v3, where these vectors are defined as follows 2 -4 w= 5 V21 - 2 -4 17 To show that w is in the subspace, express was a linear combination of v. Vz, and V3 The vector w is in the subspace spanned by V, V2, and Vy. It is given by the formula w= (O) v * (IDv. O (Simplify your answers. Type integers or...
Find a basis for and the dimension of the subspace w of R4. W = {(3s - t, s, t, s): s and t are real numbers) (a) a basis for the subspace w of R4 (b) the dimension of the subspace W of R4