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Homework Answers
ote: The norm of is denoted by |vand is calculated N a vector u Consider a subspace W of R4, W span(1, v2, v3, v4)). Where 0 из- 1. Find an orthonormal basis Qw of W and find the dimension of W 2. Fi...
ote: The norm of is denoted by |vand is calculated N a vector u Consider a subspace W of R4, W span(1, v2, v3, v4)). Where 0 из- 1. Find an orthonormal basis Qw of W and find the dimension of W 2. Find an orthonormal basis QWL of WL and find the dimension of WL 3. GIven a vector u- . find the Qw coordinate of Projw(v) . find the Qwa coordinate of Projwi (v) » find the coordinate...
1- 2- (10 points) Find the closest point to y in the subspace W spanned by...
1-
2-
(10 points) Find the closest point to y in the subspace W spanned by vì and v2. -4 -2 у 0 -1 0 -1 2 3 1 1 1 1 (10 points) The given set is a basis for a subspace W. Use 0 0 0 the Gram-Schmidt process to produce an orthogonal basis for W.
5/9/2019 the closest point to y in the subspace W spanned by u, and u Let...
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
Wite **the sum of two vectons, one in Span {u) and one in Span (wa). Assume...
Wite **the sum of two vectons, one in Span {u) and one in Span (wa). Assume that (.....) is an orthogonal besis Type an integer or simplified traction for each max element) Verity that {.uz) is an orthogonal sot, and then find the orthogonal projection of y onto Span(uz) y To verty that (0-uz) as an orthogonal set, find u, uz 2-0 (Simplify your answer.) The projection of yonte Span (0,2) 0 (Simplify your answers.) LetW be the subspace spanned...
- 21 For the set of vectors B= let H= span B. 2 13 For y...
- 21 For the set of vectors B= let H= span B. 2 13 For y = find the vector in H that is closest to y (note y&H) u N The vector in H that is closest to y is y=[
Hi, could you post solutions to the following questions. Thanks. 2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 sta...
Hi,
could you post solutions to the following questions. Thanks.
2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
the F of problem 1 and problem 2 1. For each of the following statements, say...
the F of problem 1 and problem 2
1. For each of the following statements, say whether the statement is true or false. (a) If S ST are sets of vectors, then span(S) span(T) (b) If S S T are sets of vectors, and S is linearly independent, then so are sets of vectors. then span İST. (c) Every set of vectors is a subset of a basis (d) If S is a linearly independent set of vectors, and u...
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that...
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that the following set forms a basis for W: S = -5 (B.2) Obtain the coordinate vector for A = 3 relative to S. That is, find (A)s. -8 Show work!
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that the following set forms a basis for W: S = -5 (B.2) Obtain the coordinate vector for A...
Consider the three-dimensional subspace of function space defined by the span of 1, r, and a2 the...
Consider the three-dimensional subspace of function space defined by the span of 1, r, and a2 the first three orthogonal polynomials on -1,1. Let f(x) 21, and consider the subset G-{g(z) | 〈f,g〉 0), the set of functions orthogonal to f using the L inner product on, (This can be thought of as the plane normal to f(x) in the three-dimensional function space.) Let h(z) 2-1. Find the function g(x) є G in the plane which is closest to h(x)....
Let x=(3,1,0], and let U be the subspace spanned by the orthogonal set {[1, -2, 1],[1,...
Let x=(3,1,0], and let U be the subspace spanned by the orthogonal set {[1, -2, 1],[1, 1, 1]}. Vector x can be written as X=X1+X2, where x1 is in U and xz is orthogonal to U. Find the first coordinate of x2.
ote: The norm of is denoted by |vand is calculated N a vector u Consider a subspace W of R4, W span(1, v2, v3, v4)). Where 0 из- 1. Find an orthonormal basis Qw of W and find the dimension of W 2. Find an orthonormal basis QWL of WL and find the dimension of WL 3. GIven a vector u- . find the Qw coordinate of Projw(v) . find the Qwa coordinate of Projwi (v) » find the coordinate...
1-
2-
(10 points) Find the closest point to y in the subspace W spanned by vì and v2. -4 -2 у 0 -1 0 -1 2 3 1 1 1 1 (10 points) The given set is a basis for a subspace W. Use 0 0 0 the Gram-Schmidt process to produce an orthogonal basis for 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
Wite **the sum of two vectons, one in Span {u) and one in Span (wa). Assume that (.....) is an orthogonal besis Type an integer or simplified traction for each max element) Verity that {.uz) is an orthogonal sot, and then find the orthogonal projection of y onto Span(uz) y To verty that (0-uz) as an orthogonal set, find u, uz 2-0 (Simplify your answer.) The projection of yonte Span (0,2) 0 (Simplify your answers.) LetW be the subspace spanned...
- 21 For the set of vectors B= let H= span B. 2 13 For y = find the vector in H that is closest to y (note y&H) u N The vector in H that is closest to y is y=[
Hi,
could you post solutions to the following questions. Thanks.
2. (a) Let V be a vector space on R. Give the definition of a subspace W of V 2% (b) For each of the following subsets of IR3 state whether they are subepaces of R3 or not by clearly explaining your answer. 2% 2% (c) Consider the map F : R2 → R3 defined by for any z = (zi,Z2) E R2. 3% 3% 3% 3% i. Show that...
the F of problem 1 and problem 2
1. For each of the following statements, say whether the statement is true or false. (a) If S ST are sets of vectors, then span(S) span(T) (b) If S S T are sets of vectors, and S is linearly independent, then so are sets of vectors. then span İST. (c) Every set of vectors is a subset of a basis (d) If S is a linearly independent set of vectors, and u...
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that the following set forms a basis for W: S = -5 (B.2) Obtain the coordinate vector for A = 3 relative to S. That is, find (A)s. -8 Show work!
[B] Let W be the subspace of M22 given in problem [A] . (B.1) Show that the following set forms a basis for W: S = -5 (B.2) Obtain the coordinate vector for A...
Consider the three-dimensional subspace of function space defined by the span of 1, r, and a2 the first three orthogonal polynomials on -1,1. Let f(x) 21, and consider the subset G-{g(z) | 〈f,g〉 0), the set of functions orthogonal to f using the L inner product on, (This can be thought of as the plane normal to f(x) in the three-dimensional function space.) Let h(z) 2-1. Find the function g(x) є G in the plane which is closest to h(x)....
Let x=(3,1,0], and let U be the subspace spanned by the orthogonal set {[1, -2, 1],[1, 1, 1]}. Vector x can be written as X=X1+X2, where x1 is in U and xz is orthogonal to U. Find the first coordinate of x2.
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