4 Let u-4 , v--3, w1For what value of h is w in the plane spanned...
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Let v = , u = , and let W the subspace of R4 spanned by v and u. Find a basis of W .
Instructions: 2 3 -4 3 Find V Let V be the plane spanned by the vectors UT 2 0 1
6 Let a2a28and bwhat value(s) of h is b in the plane spanned by a, and a2? 8 , and b- or what value(s) ofh is b in the plane spanne
(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.
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.
5/9/2019 the closest point to y in the subspace W spanned by u, and u Let W be the subspace spanned by 11. and u2. Write y as the sum of a vector in W and a vector orthogonal to w u, 12 13)- 12 25 3 5 6-5 | and b = | 4 l. Describe the general solution in parametric Describe all solutions of Ax = b, where A-1-2 -4 7 0 vector form
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Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that ifU W andWgU then UUW is not a subspace of V (2) Give an example of V, U and W such that U W andWgU. Explicitly verify the implication of the statement in part1). (3) Proue that UUW is a subspace of V if and only if U-W or W- (4) Give an example that proues the...
6. (20 points) Let W be a plane spanned by the vectors ői = [1, 2, 2)", T2 = (-1,1,2) (a). Find an orthonormal basis for W. (b). Extend it to an orthonormal basis of R3.
Let V = M2(R), and let U be the span of
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2. (a) Let V = M,(R), and let U be the span of s={(1 1) ($ 3). (3), (1 9). (1) 2.)} Find a basis for U contained in S. (b) Let W be the subspace of P spanned by T = {2} + 22 – 1, -2.3 + 2x +1,23 +22² + 2x – 1, 2x3 + x2 +1 -2, 4.23 + 2x2 - -4}. Find...
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6.3.8 Let W be the subspace spanned by U, and up. Write y as the sum of a vector in W and a vector orthogonal to W. -1 -2 y = un = 3 2 -1 The sum is y = y +z, where y 8. is in W and z = Doo is orthogonal to W. (Simplify your answers.)