Problem #9: Find a basis for the orthogonal complement of the subspace of R4 spanned by the following vectors.V₁ = (1, -1, 1, 6), V2 = (2,-1, 8, 4), v3 = (-1, 2, 5, -14)The required basis can be written in the form{(x, y, 1, 0), (z, w, 0, 1)}.Enter the values of x, y, z, and w (in that order) into the answer box below, separated with commas.Problem #9:

The given vectors .The aim is to find the basis for the orthogonal complement of the subspace of…

Answered: Find a basis for the orthogonal…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

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Similar questions

Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
Based on other problems I believe the dimension is 3, but I'm not sure how to find a basis given this subspace.
I need help for problem (h). Check that the set at (h) is a subspace of Rn or not.
Let V be the subspace of P^4 spanned by B = {1,x^2,x^4}. Create a chnage of basis matrix Cd,b if D = {1,x^2-9,(x^2-4)^2}. Show the mathematics involved in finding this matrix.
The sets B={[1 2 2 1]T; [1 0 2 0]T; [2 0 4 -3]T} and B'={[0 2 0 1]T; [2 1 4 -1]T; [1 2 2n 4]T} are bases for the same subspace of R4. Find the matrix M that translates B' coordinates to B coordinates.
QUESTION 1Show that W = {(a, 0, b)|a, b ∈ R} is a subspace of R3
Let ?1 = (4 3 2 1), ?2 = (−2 0 -1 0), ?3 = (0 3 0 1)a) Find the subspace of R^4 spanned by these vectors.b) Are the vectors linearly independent?c) Determine a basis for R^4 that contains as many of the above three vectors as possible.
Find a basis for the subspace of R3 spanned by S.S = {(1, 2, 2), (−1, 0, 0), (1, 1, 1)}
Find the coordinate matrix ofp = 4 − 2x2 + 3x3relative to the standard basis for P3,S = {1, x, x2, x3}.
Find the coordinate matrix of x = (−2, 1, 3) in R3 relative to the standard basis S = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}.
Suppose γ:R→R^3 is a curve such that γ^' (t)=A_γ (t) and A are a Skew-symmetric matrix. Show γ is located on a circle. If a and b are two units vector perpendicular to each other on a plane containing a circle, parametrization with γ in terms of length, and explicitly write its representation in the coordinate system (a, b).Note: The matrix A is called Skew-symmetric matrix, if we have j,i for each: A(i,j)=-A(j,i)
Suppose that S1 and S2 are subspaces of a vector space (V, F). Show that their intersection S1 ∩ S2 is also a subspace of (V, F). Is their union S1 ∪ S2 always a subspace?

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