4.4.13. Find a basis for the orthogonal complement of the following subspaces of R³: (a) the0; (b) the line in the direction (-2,1,3); (c) the image of the1 2 −1 3O2 1(d) the cokernel of the same matrix.214plane 3x + 4y – 5 zmatrix -2-2-1= 4.4.14. Find a basis for the orthogonal complement of the following subspaces of R4: (a) theset of solutions to − x+3y=2z+w = 0; (b) the subspace spanned by (1, 2, —1,3),(−2,0, 1, -2)¹, (-1,2,0,1); (c) the kernel of the matrix in Exercise 4.4.13c; (d) thecoimage of the same matrix.T

4.4.13 subpart (c) asked and answered.

Answered: 4.4.13. Find a basis for the orthogonal…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Let "W" be the set of vectors of the form below. Show that "W" is a subspace of R4. You must show all of the necessary math and cite any relevant theorems. - 2r+2s - 3t S-t r-3s-2t 2r-s+ 3t
can you please do this the matrix way because I need it to be solved the matrix way this entire problem has to be done in matrix form. I attached the question and answer
of (2, 3, 4, – 1) with B= {(1, 1, 1, 2), (1, –1, 0, 0), (0, 0, 1, 1), (0, 1, 0, 0)} of V. (R). 27. Find the coordinates respect to the basis %3D
The vector x is in a subspace H with a basis ß = {b₁, b2}. Find the ß-coordinate vector of x. = b₁ = [-2] - b₂ - [*3]-* - [15] X = 1.
4. Find a basis for the subspace spanned by the given vectors. What is the dimension of the subspace? -3 2 3 9 -6 12 2 - 1 4 2 5 -3
2. Consider vectors of the form 2y + 5y 4y у + + 5z] х 2х 8z - W = ,x, y,z are real # -x + 7z 3x + Show that the vectors form a subspace of Rt. (a) (b) Find a basis for the set.
6. Consider the space a + b+c= d H = 2а + b 3 d C R4. a + b+ 3c = 0 (a) Find a matrix A such that H = NulA. (b) Find a basis of H.
4 2. (а) Do the vectors vị = V2 = -1 V3 = -1 form a basis for R³? 1 , V3 = 3 form a basis (b) Do the vectors vị V4 = 4 V2 8. for R4? (c) For which value(s) of the constant c is the list of vectors vị = V2 = V3 = a basis of R3? ||
Can I get some help with this problem?
#6. Let W be the subspace of R³ spanned by the two vectors (1, – 1,1) and (3, – 2,0). Which one of the following vectors is a basis for W, the orthogonal complement of W? (A) (1, 1, 0) (B) (- 1,0, 1) (C) (1, 2, 1) (D) (2, 3,0) (E) (2, 3, 1)
1. Find a basis for the subspace of R4 spanned by the vectors (1,1,-4,-3), (2,0,2,-2), (2, -2,3,2)
2

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4.4.13. Find a basis for the orthogonal complement of the following subspaces of R³: 5z = 0; (b) the line in the direction (-2, 1, 3); (c) the image of the (a) the plane 3x + 4y 1 -1 3 matrix -2 2 1 (d) the cokernel of the same matrix. 1 4 2 0 −1 2