Suppose that A is an m n matrix and B is an n m matrix

Question:

Suppose that A is an m × n matrix and B is an n × m matrix where AB is a nonsingular matrix. Prove that
1. N(B) = {0}
2. C(B) ∩ N(A) = {0}
Discuss the case when m = n in connection with Theorem NPNT.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

See More Books

Question Posted: Jun 01, 2016 02:36 AM

See More Questions

Suppose that A is an m n matrix and B is an n p matrix. Prove that the null space of B is a subset of the null space of AB, that is N(B) N(AB). Provide an example where the opposite is false, in...
Suppose that A is an m n matrix and b Cm. Prove that the linear system LS(A, b) is consistent if and only if r (A) = r ([A | b]).
Suppose that A is an m n matrix with linearly independent columns and the linear system LS(A, b) is consistent. Show that this system has a unique solution.
The Sooner Equipment Company has total assets of $100 million. Of this total, $40 million was financed with common equity and $60 million with debt (both long- and short-term). Its average accounts...
The owner of an optometry practice, in a city with more than a hundred other such practices, has the following demand and cost schedules for eye exams: a. Fill in the columns for total revenue,...
After one bee left a flower with a positive charge, that bee flew away and another bee with the same amount of positive charge flew close to the plant. Which diagram in Fig. P21.100 best represents...
Consider the gasoline mileage data in Table B.3. a. Fit a multiple linear regression model relatmg gasoline mileage $y$ (miles per gallon) to engine displacement $x_{1}$ and the number of carburetor...
The unadjusted trial balance of Irvine Inn Company at December 31, 2016, and the data needed for the adjustments follow. Adjustment data at December 31 follow: a. As of December 31, Irvine Inn had...
21. DOES THE U.S DOLLAR INDEX WEAKEN IF THE US GROWTH ACCELERATES ? 22. THE U.S DOLLAR INDEX WEAKEN IF THE INTEREST RATE DIFFERENTIALS NARROW BETWEEN THOSE NATIONS ?
By what amount will the market value of a Treasury bond futures contract change if interest rates rise from 5 to 5.25 percent? The underlying Treasury bond has a duration of 10.48 years and the...
Suppose that A is an m n matrix and B is an n n nonsingular matrix. Prove that the column space of A is equal to the column space of AB, that is C(A) = C(AB).
Given the matrix A below, use the extended echelon form of A to answer each part of this problem. In each part, find a linearly independent set of vectors, S, so that the span of S, (S), equals the...
Find the adjusted balance due at maturity for a 90-day note of $15,000 at 13.8% ordinary interest if a partial payment of $5,000 is made on the 60th day of the loan.
Using the artcle below, how can the Business Relationship Manager role assist with change management in an organization? How might change management activities align with the drivers of relationship...
A brief description of Scope creep in Project Management and challenges you chose to help the reader understand what you are talking about (assume the readers do not understand the topic). Why did...
Which statement accurately describes the implications of investing in a stock with a positively skewed distribution, as projected by the company's analysis?
Components of Good Resume Personal Information Objective (optional) Highlights of Qualificatidas Experience Education Activities References TASK Create your resume
In pairs or small groups, imagine you are on the Project Management team for the construction of a new road in your city. In what ways could a PMO help you and your project? How could the project...
An ideal gas is confined to the left chamber of an insulated container. The right chamber is evacuated. A valve is opened between the chambers, allowing gas to flow into the right chamber. After...
1) The government decided to reduce taxes on fast-food to increase revenue. The government assumes that fast-food products have a) An inelastic demand b) An elastic demand c) A demand curve that is...
Verify that |z= |z|2| of for (a) z = 2 - 4i (b) z = - 3 + 5i
In each part, use the formula in Theorem 1.4.5 to compute the inverse of the matrix, and check your result by showing that AA-1 = A-1 A = I. (a) A=
In each part, use the method of Example 4 in Section 1.5 to find and check your result by showing that AA-1 = A-1 A = I. (a) 1 1i 0 A=101 -i 1-2i 2
Popular furniture company, IKEA, has purchased forests in Romania as well as land in Alabama to assist with keeping up with the wood demand necessary to complete customer orders. This was one way...
How does China being Turkey's biggest import partner affect Turkey's exchange rate?
Assignment 4 In this assignment you are provided information on an experiment and you are required to investigate and interpret the output which is provided below. Problem: Consider the...

Suppose that A is an m n matrix and B is an n m matrix

Question:

Step by Step Answer:

First 0 NB trivially Now suppose that x NB Then ABx A Bx Theorem MMA A0 x NB 0 Theorem MMZM S...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions