Question: Let u, v R n be two fixed vectors such that Question 1: (5 Marks) Let u, v E R be two fixed vectors such

Let u, v R n be two fixed vectors such that

Question 1: (5 Marks) Let u, v E R" be two fixed vectors such that (ulv) # 0, where (.|.) is the standard inner product on R". Define T : R" -> R" by T(x) = (xv)u. Then (a) Show that T is a linear operator on R". (b) Prove/ disprove: T is diagonalizable

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!

Ryan Ren Assignment Homework 2 due 09/14/2017 at 02:15pm PDT 1. (1 pt) Compute the following product. \u0014 \u0015\u0014 \u0015 \u0014 5 0 4 7 4 = 0 7 1 7 7 Math4A-02-M17-Wen \u0015 Answer(s)...

Problem 1. (1 point) Let 6 8 12 $1- 6 ,V2 20 ,V3 21 2 ~12 7 Is the set {V1, v2, V3} linearly independent? 0 A. Yes 0 B. No If the vectors are linearly dependent, nd coefficients, not all zero, that...

Linear algebra question. Let u, v, W be (fixed, but unknown) vectors in IR" and let A be an n x n matrix (fixed, but unknown). (a) (3 marks) Prove the following statement: If u, v, W are linearly...

1) Let In be the line through the points (1, 0, -1) and (-1, 1, 0), and let L2 be the line through the points (3, 1, -1) and (4, 5, -2). Show that I and Ly are skew, and then find the distance...

Need Detailed Explanation of these Questions from 1 to Question 8 and there all parts, this is my last question do it correctly please or I'll not only give you a dislike but also will report you and...

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2015 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

- 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...

M lab - a.( X Edufide X G G gmail - X C image X Design X G curvatu X curvatu X M Math - X G math fc x e OA12 ( X Dashbc X C Let L:R X V X...

Question 1 (17 marks) a) Show that the function (V1, V2) = 2WW2 + X142 - y192 + 2122 defined for any vectors v1 = (T1, y1, 21, w1 ) and v2 = (12, 32, 22, W2) in vector space R4 is not an inner...

M lab - a.( X Edufide x G G gmail - x C image X Design X G curvatu x curvatu X M Math - X G math fc x e OA12 ( X Dashbc X C Let L:R X V X C...

A car moves with constant speed around the circle shown below. When it is at point A its coordinates are x = 0, y = 3 m and its velocity is (-6im/s). When it is at point B its velocity and...

Robin Design, Inc. is a Web site design and consulting firm. The firm uses a job order costing system in which each client is a different job. Robin Design assigns direct labor, licensing costs, and...

Which of the following agencies is referred to as the "congressional watchdog" because of its role in the US . legislative branch presenting ics findings and recommendations so Congress? Select one:...

Question 1 The Supermarket Store is about to place an order for Halloween candy. One best-selling brand of candy can be purchased at $ 2.50 per box before and up to Halloween. After Halloween, all...