Question: (a) If I is the 4 4 matrix with every entry 1, show that I - 1/2 J is self-inverse and symmetric. (b) If

(a) If I is the 4 × 4 matrix with every entry 1, show that I - 1/2 J is self-inverse and symmetric.
(b) If X is n × m and satisfies XTX = lm, show that Im,-2XXT is self-inverse and symmetric.

Step by Step Solution

★★★★★

3.43 Rating (150 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

b Write U In 2XXT Then U is symmetric b... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

950-M-L-A-L-S (6246).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Find the eigenvalues and eigenvectors of an n x n matrix with every entry equal to 1.

(a) Prove that every real 3 3 matrix has at least one real eigenvalue. (b) Find a real 4 4 matrix with no real eigenvalues. (c) Can you find a real 5 5 matrix with no real eigenvalues?

A small community organization consists of 20 families, of which 4 have one child, 8 have two children, 5 have three children, 2 have four children, and 1 has five children. (a) If one of these...

6. Let A = {x E Z |x 2 5a + 2 for some integer a}, B = {y E Z | y = 10!) 3 for some integer b}, and C = {z E Z | z = 106 + 7 for some integer C}. Prove or disprove each of the following statements....

Question: Please help keep getting it wrong! According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg. Assume that blood...

Solve attached Correlation and Linear Regression It is widely believed that the more education one receives the higher the income earned at the time of first employment and over the course of a...

Consider the following time series data Problem 15-05 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6 Value 19 14 17 12 17 14 a. Choose the correct time series plot. (1) (iI)...

Birth and death process 4. Vehicles arrive in College Station for football weekends at varying rates. Cars arrive according to a Poisson process with rate A = 3 per minute, trucks arrive according to...

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...

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...

Gary and Gertrude are married on April 8, 2010. They use Gertrudes home as their residence. Gertrude purchased the home on November 14, 2008, for $60,000. On February 19, 2011, Gertrude is killed in...

Write a structural formula for the most stable conformation of each of the following compounds: (a) 2, 2, 5, 5-Tetramethylhexane (Newman projection of conformation about C-3C-4 bond) (b) 2, 2, 5,...

. Given that directors have broad powers over company decisions, how can companies ensure that directors exercise their authority responsibly while safeguarding shareholder interests?

Which of the following statements is true? a. Demand-pull inflation is caused by excess total spending. b. Cost-push inflation is caused by an increase in resource costs. c. If nominal interest rates...

Show that defines a norm on Rn. llxlloc max l.ril lsisn

Let x and y be vectors in an inner product space. Show that if x y then the distance between x and y is (||x||2 + ||y||2)1/2

Let x Rn. Show that ||x||

Youre trying to choose between two different investments, both of which have up-front costs of $91,000. Investment G returns $156,000 in 8 years. Investment H returns $276,000 in 15 years. Required:...

9. Returns and Variances (LO1, 2) Consider the following information: a. What is the expected return on an equally weighted portfolio of these three stocks? b. What is the variance of a portfolio...

AFT'I SHal IU) CX Enterprises has the following expected dividends: $1.08 in one year $1.16 in two years, and $1.28 in three years. After that, its dividends are expected to grow at 3.7% per year...