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Texts: Problem 6: The Orthogonal Complement is a SubspaceLet ... | Filo

Texts: Problem 6: The Orthogonal Complement is a SubspaceLet ... | Filo

11 个月之前

SOLVED: Let X = [a, b, c]. Let U be the subspace spanned by the orthogonal basis u = [1, 1, 1], v = [1, -1, 0], w = [1, 1, -2]. Find the coefficient of u when expressing X as a linear combination of u, v, w.Select one: (a b c)/3b: a b cc: 1/3d: aNone of the other choices is correct.

SOLVED: Let X = [a, b, c]. Let U be the subspace spanned by the orthogonal basis u = [1, 1, 1], v = [1, -1, 0], w = [1, 1, -2]. Find the coefficient of u when expressing X as a linear combination of u, v, w.Select one: (a b c)/3b: a b cc: 1/3d: aNone of the other choices is correct.

2021年12月16日

Find the orthogonal projection of-192017onto the subspace W... | Filo

Find the orthogonal projection of-192017onto the subspace W... | Filo

已浏览 5232 次7 个月之前

Answered: Find an orthogonal basis for the subspace {(x, y, z) E R³ | x + 4y – 2z = 0} - | bartleby

Answered: Find an orthogonal basis for the subspace {(x, y, z) E R³ | x + 4y – 2z = 0} - | bartleby

(a) Prove that the set of all 3 -vectors orthogonal to [1,-1,4] forms a subspace of ℝ^3. (b) Is the subspace from part (a) all of ℝ^3, a plane passing through the origin in ℝ^3, or a line passing through the origin in ℝ^3 ? | Numerade

(a) Prove that the set of all 3 -vectors orthogonal to [1,-1,4] forms a subspace of ℝ^3. (b) Is the subspace from part (a) all of ℝ^3, a plane passing through the origin in ℝ^3, or a line passing through the origin in ℝ^3 ? | Numerade

2023年6月6日

If 𝐕 is the subspace spanned by (1,1,0,1) and (0,0,1,0), find (a) a basis for the orthogonal complement 𝐕^⊥. (b) the projection matrix P onto 𝐕. (c) the vector in 𝐕 closest to the vector b=(0,1,0,-1) in 𝐕^⊥. | Numerade

If 𝐕 is the subspace spanned by (1,1,0,1) and (0,0,1,0), find (a) a basis for the orthogonal complement 𝐕^⊥. (b) the projection matrix P onto 𝐕. (c) the vector in 𝐕 closest to the vector b=(0,1,0,-1) in 𝐕^⊥. | Numerade

2021年11月7日

let w be the subspace spanned by u1 and u2 write y as the sum of a vector in w and a vector orthogonal to w u2 35 the sum is yy 2 where y is in w and z is orthogonal to w 95085

let w be the subspace spanned by u1 and u2 write y as the sum of a vector in w and a vector orthogonal to w u2 35 the sum is yy 2 where y is in w and z is orthogonal to w 95085

2021年10月22日

If V is the subspace spanned by (1,0,1,0,1), (1,1,0,1,1), and (0,0,1,0,1), find Matrix A which has the orthogonal complement V1 as the nullspace. Find a basis for the orthogonal complement V. What are the dimensions of each subspace V and orthogonal complement V? What dimensions of subspace are orthogonal to subspace V? (Please include a mathematical proof) Find Matrix A which has orthogonal complement V as left nullspace.

2021年10月20日

Let W be the subspace of 𝐑^5 spanned by u=(1,2,3,-1,2) and v=(2,4,7,2,-1) . Find a basis of the orthogonal complement W^⊥ of W We seck all vectors w=(x, y, z, s, t) such that ⟨ w, u⟩=x 2 y 3 z-s 2 t=0 ⟨ w, v⟩=2 x 4 y 7 z 2 s-t=0 Eliminating x from the second equation, we find the equivalent system x 2 y 3 z-s 2 t=0 z 4 s-5 t=0 The free variables are y, s, and t . Therefore, (1) Set y=-1, s=0, t=0 to obtain the solution w1=(2,-1,0,0,0) (2) Set y=0, s=1, t=0 to find the so

2020年6月14日

Let W be the subspace of R^2 spanned by the vector (3,4). Using the standard inner product, let E be the orthogonal projection of R^2 onto W. Find (a) a formula for E(x1, x2) (b) the matrix of E in the standard ordered basis; (c) W^⊥; (d) an orthonormal basis in which E is represented by the matrix [ 1 0 0 0] . | Numerade

2022年11月19日

Construct any 2 by 3 matrix of rank 1. Copy Figure 2.5 and put one vector in each subspace (two in the nullspace). Which vectors are orthogonal? | Numerade

2021年11月7日

SOLVED:Let V be the space C[-1,1] with the inner product of Example 7 . Find an orthogonal basis for the subspace spanned by the polynomials 1, t, and t^{2} . The polynomials in this basis are called Legendre polynomials.

2020年5月12日

Let V be the space C[-2,2] with the inner product of Example 7 . Find an orthogonal basis for the subspace spanned by the polynomials 1, t, and t^2 . | Numerade

2020年5月12日

Find a polynomial p3 such that {p0, p1, p2, p3} (see Exercise 11) is an orthogonal basis for the subspace ℙ3 of ℙ4 . Scale the polynomial p3 so that its vector of values is (-1,2,0,-2,1) | Numerade

2020年5月12日

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