Suppose that A is a square matrix, and B is a matrix in reduced row-echelon form that

Question:

Suppose that A is a square matrix, and B is a matrix in reduced row-echelon form that is row-equivalent to A. Prove that if A is singular, then the last row of B is a zero row.

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 02:32 AM

See More Questions

Suppose that A is a square matrix of size n n and that we know there is a single vector b Cn such that the system LS(A, b) has a unique solution. Prove that A is a nonsingular matrix.
Suppose that A is a square matrix and there is a vector, b, such that LS(A, b) has a unique solution. Prove that A is nonsingular. Give a direct proof (perhaps appealing to Theorem PSPHS) rather than...
Suppose that A is a square matrix. Prove that the constant term of the characteristic polynomial of A is equal to the determinant of A.
Sung Corporation, a clothing retailer, engaged in the transactions listed in the first column of the table below. Opposite each transaction is a ratio and space to mark the effect of each transaction...
Define signaling and screening and give an example of each.
A 15.0-kg block is attached to a very light horizontal spring of force constant 500.0 N/m and is resting on a frictionless horizontal table (Fig. E8.44). Suddenly it is struck by a 3.00-kg stone...
Data 2.7 on page 95 introduces the dataset HollywoodMovies, which contains information on more than 900 movies that came out of Hollywood between 2007 and 2013. One of the variables is the budget (in...
Dan and Patricia form Crane Corporation. Dan transfers land (worth $200,000, basis of $60,000) for 50% of the stock in Crane. Patricia transfers machinery (worth $150,000, adjusted basis of $30,000)...
Research System Incident and Event Manager (SIEM). I need a basic description including what it is, how it helps security, and what devices should it monitor. Explain.
1. Which barriers to entry contributed most to Tata Motors lack of success with the original Nano? 2. Which macroenvironment factors did Tata Motors consider when adjusting the marketing and...
Say as much as possible about each system's solution set. Be sure to make it clear which theorems you are using to reach your conclusions. 1. 6 equations in 6 variables, singular coefficient matrix....
Suppose that A is a nonsingular matrix and A is row-equivalent to the matrix B. Prove that B is nonsingular.
Go to Entrepreneur franchise zone web page at http://www.entrepreneur.com/franchise500 and view the top 500 franchises for the past year. How many of these retailers in the top 10 have you patronized...
How would you describe each dimension of EI, and then explain how EI may be used in unethical ways. How would you Define organizational citizenship behavior (OCB) & then list five specific behaviors...
Draw and label a graph illustrating a demand and supply of anything. Show how an increase in supply and a decrease in demand could result in a lower equilibrium price and a lower equilibrium quantity.
You are given the following production function Q = K 1/3 L 2/3 , where Q is output, L is labor, and K is capital. First, calculate the marginal product of capital and the marginal product of labor....
10. Smile Collection, a local dentistry clinic, installed a brand new dental chair. The electrical work required to prepare for the installation was $18,000. The invoice price of the equipment...
One policy and procedure that is already firmly in place at Zappa Electronics is that whenever there is a workplace incident, a formal Incident Report must be completed in detail and kept in a risk...
When a wave passes from one medium into another, which of these quantities must stay the same? (a) Wavelength (b) Wave speed (c) Frequency (d) Direction of propagation
Select the correct answer for each of the following questions. 1. On December 31, 20X3, Saxe Corporation was merged into Poe Corporation. In the business combination, Poe issued 200,000 shares of its...
What do the lines r = r0 + tv and r = r0 - tv have in common? Explain.
Let r1 and r2 be vectors from the origin to the points P1(x1, y1, z1) and P2(x2, y2, z2), respectively. What does the equation r = (1 - t)r1 + tr2 (0 t 1) represent geometrically? Explain your...
Determine whether the planes are parallel. (a) 4x - y + 2z = 5 and 7x - 3y + 4z = 8 (b) x - 4y - 3z - 2 = 0 and 3x - 12y - 9z - 1 = 0
Solve (2.4 x 10-5) X 875 (2.5 x 107) x (2.8 x 107)
assume there are no outliers. Draw the boxplot for the following frequency table. You may X f rf cf crf 3 7 0.1228 7 0.1228 4 11 0.1930 18 0.3158 5 9 0.1579 27 0.4737 618 6 0.1053 33 0.5789 10 0.1754...
Find the partial derivative of the regularized least squares problem: {) (w + x) (wo + w x ( ) + w x ( ) } + |/\||[w1, w2]|| with respect to wo, w, and w2. Although there is a closed-form solution to...

Suppose that A is a square matrix, and B is a matrix in reduced row-echelon form that

Question:

Step by Step Answer:

Let n denote the size of the square matrix A By Theorem NMRR...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions