Question: Let u be some fixed factor in R^n and let S be the set of all vectors in R^n that are orthogonal to u. Is

Let u be some fixed factor in R^n and let S be the set of all vectors in R^n that are orthogonal to u. Is S a sub space of R^n?

Question 18 15 pts Let u be some fixed vector in R" and let S' be the set of all vectors in " that are orthogonal to u. Is S a subspace of R"? Be sure to justify your answer by showing explicitly how it either passes all the part of the subspace test or how it fails one of them. (Submit your work as a JPEG, PDF or PNG file below.)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Let u be a fixed vector in Rn. Prove that the set of all vectors in Rn that are orthogonal to u is a subspace of Rn.

Let u be a unit vector in R n , and let B = uu T .a. Given any x in R n , compute Bx and show that Bx is the orthogonal projection of x onto u, as described in Section 6.2. b. Show that B is a...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

please help to answer these 8 questions, thank you~ Question 1. In each of the following, determine if the given set is a subspace of R2 or not. For each case in which the set is a subspace, verify...

- Symbolic functions must be entered using notation similar to the examples given below. - Do NOT include the name of the function or an equal sign. {i.e., do NOT include anything like '1' =' in your...

Q8\ 4 Points\ Let vec(e)_(i) denote the standard basis in R^(n) .\ Vectors vec(v) and vec(u) in space R^(4) satisfy the following conditions:\ both of them are orthogonal to vec(e)_(3) and vec(e)_(4)...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Chapter 6.1 Write on paper for upvote. questions: 23, 25, 37, 41 please 10. U = [_3 31. =18 8] 27. a. (2v - w, 3u + 2w) b. llu + vil In Exercises 11-12, find the standard inner product on P2 of the...

3 In 0900'0 500O'D 1000 0 FIG. 4. Process H alloy composition: (a) & chart, (b) "chart based on log ratios, (o) X' versus 73. S 0900'0 50COD 100070 S602 R. A. Boyles For this data set, step (3) in...

hi. kindly assist with working out/ calculations for these adjustments. ADJUSTMENTS AND ADDITIONAL INFORMATION 1. The tenant has paid her March 2022 rent in advance. NB: the monthly rent had been...

You've just turned 20 years old today. You would like to finish your Cal Poly degree, then work for a few years, and then start your grad school when you turn 26. To save up enough for your grad...

what is the primary type of investment insurers used to back their traditional fixed annuity products

A company is preparing completing their Cash Budget. The following data has been prepared for cash receipts and payments. January February March Cash receipts $1,061,200 $1,182,400 $1,091,700 Cash...