If A and B are n x n matrices, show that they have the same null space

Question:

If A and B are n x n matrices, show that they have the same null space if and only if A = UB for some invertible matrix U.
[Hint: Exercise 28 §7.3.]

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

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra With Applications

ISBN: 9780070985100

7th Edition

Authors: W. Keith Nicholson

See More Books

Question Posted: Jun 21, 2016 06:49 AM

See More Questions

In this exercise we consider how to generate matrices with specified ranks using MATLAB. (a) In general, if A is an m n matrix with rank r, then r min(m, n). Why? Explain. If the entries of A are...
Show that if A and B are two n x n matrices that both have the same diagonalizing matrix X. then AB = BA.
A spatial Poisson process is a model for the distribution of points in two dimensional space. For a set A R 2 , let N A denote the number of points in A. The two defining properties of a spatial...
State the issues presented to the Court in McCord v. McCord .
What are slack, surplus, and artificial variables? When is each used, and why? What value does each carry in the objective function?
What are the relevant costs to be considered when deciding whether to take a quantity discount? On what basis should the decision be made?
Charisma of top-level leaders. Refer to the Academy of Management Journal (August 2015) study of whether the charisma of top leaders impacts performance, Exercise 11.28 (p. 661). Based on data...
The 12 partners of a regional public accounting firm met in special session to discuss audit engagement efficiency. Jones spoke up, saying, We all certainly appreciate the firm wide policies set up...
8 In business forecasting, what is usually considered a long-term time period? O Ten years or longer O Three months or longer O One year or long Six months or longer OTwo years or longer
A software developer is using a microphone and a sound editing app to collect and edit sounds for his new game. When collecting sounds, the software developer can decide on the sampling resolution he...
In each case find PD b, where B and ordered bases of V. Then verily that CD(v) = PD BCBW- (a) F= R2, B = f(0,-l),(2, 1)} D = ((0, 1),(1, I)}, v = (3,-5) (b) V= P2, B = [1 + x + x2}, D = {2, x + 3,...
Given a complex number w, define TU: C C by Tz ,(z) = wz for all z in C. (a) Show that Tu, is a linear operator for each w in C, viewing C as a real vector space. (b) If B is any ordered basis of C,...
Is it possible for a product manager to have the same degree of tunnel vision that a project manager has? If so, under what circumstances?
Among 450 randomly selected drivers in the 16 - 18 age bracket, 374 were in a car crash in the last year. If a driver in that age bracket is randomly selected, what is the approximate probability...
Construct a 90% confidence interval for the population standard deviation o at Bank A. Bank A 6.4 6.6 6.7 6.8 7.1 7.2 7.6 7.8 7.8 7.8
In 2002, after the accounting deceptions of the management of many multi-million dollar corporations (with Enron being the benchmark name of that time period), the Security and Exchange Commission...
1.Deduce the structure of a compound with molecular formula CsH100 that exhibits the following IR, H NMR, and 13C NMR spectra. Data from the mass spectrum are also provided. Mass Spec. Data relative...
Transcribed image text: Prots Caco.ch Part 2 Income Statement Med Earningstemet Tante Sheet For the event.com Competence ended The fram C an an dy wana A TO nede ANG ore.com wwwwww og for to...
Copper reacts with sulfuric acid according to the following equation: How many grams of sulfur dioxide are created by this reaction if 14.2 g of copper reacts with 18.0 g of sulfuric acid? 2 HSO4 +...
Show, if u(x, y) and v(x, y) are harmonic functions, that u + v must be a harmonic function but that uv need not be a harmonic function. Is e"e" a harmonic function?
In Exercises, find a basis for the eigenspace associated with A for each given matrix. (a) (b) 3 0 0 3-21,A=3 -2 2 0052 0020 2300
Let L: P1 P1 be the linear operator defined by L(at + b) = bt + a. Using the matrix representing L with respect to the basis {1, t} for P1, find the eigenvalues and associated eigenvectors of L?
Prove that if is an eigenvalue of a matrix A with associated eigenvector x, and k is a positive integer, then k is an eigenvalue of the matrix Ak = A ( A ...... A (k factor) With associated...
During 2024, its first year of operations, Hollis Industries recorded sales of $11,900,000 and experienced returns of $760,000. Cost of goods sold totaled $7,140,000 (60% of sales). The company...
What is the value of a 15% coupon bond with 11% return? Is it a discount or a premium bond?
A manufacturer with a December 31 taxation year end sells new machinery for $50,000 on January 2, 2022. The cost of the machinery is $20,000. The terms of the sale require an initial payment of...

If A and B are n x n matrices, show that they have the same null space

Question:

Step by Step Answer:

Assume that A and B are both n n and that null A null B Define T A ...View the full answer

Linear Algebra With Applications

Students also viewed these Linear Algebra questions