Prove the following corollary to the Rank Theorem: Let A be an m n matrix with
Question:
Prove the following corollary to the Rank Theorem:
Let A be an m × n matrix with entries in Zp. Any consistent system of linear equations with coefficient matrix A has exactly pn-rank(A) solutions over Zp.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 62% (8 reviews)
Recall the Rank Theorem which applies to systems over Z p not just R n says If the sy...View the full answer
Answered By
Ayush Mishra
I am a certified online tutor, with more than 3 years of experience in online tutoring. My tutoring subjects include: Physics, Mathematics and Mechanical engineering. I have also been awarded as best tutor for year 2019 in my previous organisation. Being a Mechanical Engineer, I love to tell the application of the concepts of science and mathematics in the real world. This help students to develop interest and makes learning fun and easy. This in turn, automatically improves their grades in the subject. I teach students to get prepared for college entry level exam. I also use to teach undergraduate students and guide them through their career aim.
5.00+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Prove the following corollary to the Rank Theorem: Let A be an m X n matrix with entries in
-
Let A be an m n matrix with rank equal to n. Show that if x 0 and y = Ax, then y 0.
-
Let A be an m ( n matrix with linearly independent columns and let A = QR be a QR factorization of A. Show that A and Q have the same column space.
-
50 successes in 200 trials when p = 0.2. For the binomial experiments find the normal approximation for the probability of
-
Consider a potential employee who values wages but also values the opportunity to pursue non-work related activities. (You may think of these activities as relating to family obligations, such as...
-
Aspen Industries became a corporation in the state of Colorado on March 23, 2015. The company was authorized to issue 1 million shares of $6 par value common stock. Since the date of incorporation,...
-
Cameron Company (70% WI) and Garcia Company (30% WI) own a joint working interest in the Dowling Field. There is a 1/8 royalty owner. The 1/8 royalty is shared proportionally by Cameron and Garcia....
-
List three types of consulting services that audit firms are now prohibited from providing to clients that are public companies. For each item, indicate the specific threats, if any, that the...
-
Question 6 of 29 (1 point) | Attempt 1 of 1 | 3h 26m Remaining Write the statement in words. Let p = "The plane is on time." Let q= "The sky is clear." q-p Choose the correct statement in words....
-
During the month of April, the molding department of Patterson Foundry completed and transferred out 28,000 units. At the end of April, there were 10,000 units in process, 60 percent complete....
-
Solve the systems of linear equations over the indicated Z p . x 1 + 4x 4 = 1 over Z 5 x 1 + 2x 2 + 4x 3 = 3 2x 1 + 2x 2 + x 4 = 1 x 1 + 3x 3 = 2
-
When p is not prime, extra care is needed in solving a linear system (or, indeed, any equation) over Z p . Using Gaussian elimination, solve the following system over Z 6 . What complications arise?...
-
A data set with whole number has a low value of 20 and a high value of 82. Find the class width and class limits for a frequency table with 7 classes.
-
As stated in a class handout on the strategy of competition and cooperation that is posted in Module 9: "Economists have a simple view of cooperation and conflict: People tend to cooperate when they...
-
Wayne Co. has the following Income Statement (in millions): Wayne Co. Income Statement For the Year Ended December 31, 2023 Net Sales $160 Cost of Goods Sold 100 Gross Profit 60 40 $ 20 Operating...
-
Discuss the conditions of taking out a loan with the IMF or World Bank- there are specific things a country must do- detail them Why were the Jamaican farmers (vegetable/dairy/banana) unable to...
-
If the nominal rate of return is 8.08% and the inflation rate is 3.99%, by what percent is actual purchasing power increasing?
-
Discuss the challenges and opportunities in the application of Building Information Modeling (BIM) for collaborative design and construction management in large-scale infrastructure projects .
-
National Express reports the following costs and expenses in June 2020 for its delivery service (amounts are in thousands). Instructions Determine the total amount of (a) delivery service (product)...
-
Describe a job you have had in the past or a job you are very familiar with. Indicate the negative aspects of the job and how it could be improved with current human resource management techniques.
-
In Exercises 11-14, calculate the positive eigenvalue and a corresponding positive eigenvector of the Leslie matrix L. 1. 2. 3. 4. 20 1 1.5 0.5 0 400 700 1e 300 5023
-
If a Leslie matrix has a unique positive eigenvalue 1, what is the significance for the population if is 1 > 1? 1 > 1? 1 = 1?
-
Verify that the characteristic polynomial of the Leslie matrix L in Equation (3) is cL() = (-1)n(n - b1 n-1 - b2s1 n-2 - b3s1s2 n-3 - - bns1s2 sn-1)
-
Why are revenue and expense accounts called temporary? Are there other temporary accounts
-
1.Kathy Morris owns a small decorating business called Premium Decorating. A partiallycompleted worksheet for Premium Decorating and additional information follow directly.Additional Information1....
-
If compliance with the continuing education requirement is by self-attestation, proof of participation in required continuing education is the responsibility of the licensee. To ensure that proof of...
Study smarter with the SolutionInn App