Let A be an m n matrix. (a) If B is a nonsingular m in
Question:
(a) If B is a nonsingular m × in matrix, show that BA and A have the same nullspace and hence the same rank.
(b) If C is a nonsingular n × n matrix, show that AC and A have the same rank.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 40% (5 reviews)
a If x NA then BAx B0 0 and hence x NBA Thus NA is a subspace of NBA On the other hand if x ...View the full answer
Answered By
Muhammad Salman Alvi
Well, I am a student of Electrical Engineeing from Information Technology University of Punjab. Just getting into my final year. I have always been good at doing Mathematics, Physics, hardware and technical subjects. Teaching profession requires a alot of responsibilities and challenges.
My teaching experience started as an home tutor a year ago. When I started teaching mathematics and physic subjects to an O Level student. He was about 14 years old. His name was Ibrahim and I used to teach him for about 2 hours daily. Teaching him required a lot of patience but I had to be polite with him. I used to give him a 5 min break after 1 hour session. He was quite weak in basic maths and calculation. He used to do quite a lot of mistakes in his homework which I gave him weekly. So I decided to teach him basics from scratch. He used to say that he got the concept even if he didn't. So I had to ask him again and again. I worked on his basics for a month and after that I started taking a weekly test sesions. After few months he started to improve gradually. Now after teaching him for about a year I can proudly say that he has improved alot. The most important thing was he managed to communicate all the difficullties he was facing. He was quite capable and patient. I had a sincere desire to help him reach to its full potential. So I managed to do that. We had a very good honest relationship of a student and a teacher. I loved teaching him as a tutor. Now having an experience of one year teaching I can read students quite well. I look forward to work as an online tutor who could help students in solving their all sort of difficulties, problems and queries.
4.90+
29+ Reviews
43+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Let A be an m n matrix with linearly independent columns. Explain why ATA must be an invertible matrix. Must AAT also be invertible? Explain.
-
Let A be an m n matrix and c be a nonzero vector in n. Then exactly one of the following systems has a solution: Either I Ax = 0 and cTx > 0 for some x n+ or II ATy c for some y m.
-
Let A be an m n matrix, V an n r matrix, and B an m r matrix. Show that AX = B if and only if Axj = bj, j = 1,..., r
-
What freedom does an international organisation have in regard to imposing its own approaches to HRM on its operations throughout the world? How can an international organisation, aware of the need...
-
The yield on a corporate bond is 10%, and it is currently selling at par. The marginal tax rate is 20%. A par value municipal bond with a coupon rate of 8.50% is available. Which security is a better...
-
The ratio of shear modulus to the modulus of elasticity, if Poisson's ratio is 0.25 , will be (a) 0.40 (b) 0.25 (c) 4.00 (d) 0.50
-
What is a PRR and what is it intended to accomplish?
-
On October 1, 2012, Faith Schultz established Heavenly Realty, which completed the following transactions during the month: a. Faith Schultz transferred cash from a personal bank account to an...
-
What ethical considerations must be taken into account during conflict resolution, and how can mediators ensure that resolutions are both fair and sustainable ?
-
Jimmy owns a garden in which he has planted N trees in a row. After a few years, the trees have grown up and now they have different heights. Jimmy pays much attention to the aesthetics of his...
-
Prove that a linear system Ax = b is consistent if and only if the rank of (A | b) equals the rank of A.
-
Prove Corollary 3.6.4.
-
In Exercises solve for x or b. (a) log 10 1000 = x (b) log 10 0.1 = x
-
On November 17, 1991, the Home News of central New Jersey used the bar chart in the accompanying figure to show the 19801991 passenger traffic trends for Newark International Airport. (a) Use these...
-
F is a partner in an investment partnership. She receives a payment equal to 10% of the partnerships income in exchange for advising services rendered to the partnership. In the current year, the...
-
You are given the following information about two stocks: (a) Calculate the mean and standard deviation for each stock. (b) Compare the mean, standard deviation, and coefficient of variation of each...
-
Your family started a new manufacturing business making outdoor benches for use in parks and outdoor venues two years ago. The business has been very successful, and sales are soaring. Because of...
-
Q is a 20 percent member in Lynn Properties, LLC. Because she is more involved than the other members in the LLC's activities, she receives a guaranteed payment from the LLC in the amount of $25,000...
-
Define and explain the differences between the following terms. a . Law and theory b . Theory and experiment c . Qualitative and quantitative d . Hypothesis and theory
-
How will relating product contribution margin s to the amount of the constrained resource they consume help a company maximize its profits?
-
Verify that if P is a k k regular transition matrix all of whose row sums are equal to 1, then the entries of its steady-state vector are all equal to 1 / k.
-
John is either happy or sad. If he is happy one day, then he is happy the next day four times out of five. If he is sad one day, then he is sad the next day one time out of three. Over the long term,...
-
Construct the vertex matrix for each of the directed graphs illustrated in the accompanying figure. (a) (b) (c) Ps
-
Stock #1 has a standard deviation of 55 percent. Stock #2 has a standard deviation of 75 percent. You invest 48 percent of your money in Stock #1 and the rest in Stock #2. If there were NO benefit to...
-
Eagle Industries' bonds have a 10-year maturity and a 8.00% coupon paid semiannually. They sell at their $1,000 par value, and are not callable. What s the effective annual rate (EFF %) for these...
-
Help Save & Ext The following transactions occur for the Panther Detective Agency during the month of July 1. Purchase a truck and sign a note payable, $13,900 2. Purchase office supplies for cash,...
Study smarter with the SolutionInn App