Let A be an n n matrix. Prove that the following statements are equivalent. (a) N(A)
Question:
(a) N(A) = {0}.
(b) A is nonsingular.
(c) For each b ∊ Rn, the system Ax = b has a unique solution.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 76% (13 reviews)
a Implies b If N A 0 then Ax 0 has only the trivial solution x 0 By The...View the full answer
Answered By
Muhammad Haroon
More than 3 years experience in teaching undergraduate and graduate level courses which includes Object Oriented Programming, Data Structures, Algorithms, Database Systems, Theory of Automata, Theory of Computation, Database Administration, Web Technologies etc.
5.00+
3+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Linear Algebra questions
-
Let Ω be a three-dimensional region and F: Q R3 be C1 on Q. Suppose further that, for each (x, y, z) Ω, both the line segments L((x, y, 0); (x, y, z)) and L((x, 0, 0); (x, y,...
-
Let A be an m ( n matrix. Prove that if AT A is nonsingular, then rank A = n.
-
Let A be an n x n skew symmetric matrix. Prove that xT Ax = 0 for all x in Rn.
-
How do researchers investigate the effectiveness of the integrated reporting initiative?
-
Compute the required monthly payment on an $80,000 30-year fixed-rate mortgage with a nominal interest rate of 5.80%. How much of the payment goes toward principal and interest during the first year?
-
Currently, the Social Security and Medicare programs are funded by payroll taxes rather than by the federal personal income tax. In 2019, the payroll tax for Social Security was 12.4 percent on wage,...
-
Explain what modulo 12 means.
-
On January 1, 2008, Titania Inc. granted stock options to officers and key employees for the purchase of 20,000 shares of the companys $10 par common stock at $25 per share. The options were...
-
Computerized Accounting Coursework 1 This assignment should be done in groups of 4 -5. It represents 25% of your final grade. Scenario Julie runs a small retail business selling handmade clothing...
-
Based on Problem 2-9B, prepare an income statement for David Segal for the month of October 20. Problem 2-9B: David Segal started a business. During the first month (October 20--), the following...
-
Prove that if S is a subspace of R1 either S = {0} or S = R1.
-
Let U and V be subspaces of a vector space W. Prove that their intersection U V is also a subspace of W.
-
Carbon dioxide has attracted much recent interest as a greenhouse gas. Determine the vibrational contribution to C V for CO 2 , where 1 = 2349 cm -1 , 2 = 667 cm -1 (doubly degenerate), and 3 =...
-
You plan to save $320 per month starting today for the next 41 years "just to start the month off right." You feel that you can earn an interest rate of 10.2 percent compounded monthly. How much will...
-
You have just won the lottery and will receive a lump sumpayment of $22.65 million after taxes. Instead of immediately spending your money, you plan to deposit all of the money into an account that...
-
SIMPLE PROCESS COSTING AND INCOMPLETE UNIT (CLOSING) Ultimate Sdn Bhd manufactures organic fertiliser by means of two successive processes, Process A and Process B. Below is the costs involved for...
-
The following is a part of unadjusted trial balance for RAM company which establishment in 0 1 / 0 1 / 2 0 2 0 when authorized to issue 1 , 0 0 0 , 0 0 0 ordinary at par $ 2 and 1 0 0 , 0 0 0 @ 2 0 5...
-
To fund your dream around-the-worldvacation, you plan to save $1,375 per year for the next 11 years starting one year from now. If you can earn an interest rate of 6.01 percent, how much will you...
-
What are the CVP assumptions?
-
When you weigh yourself on good old terra firma (solid ground), your weight is 142 lb. In an elevator your apparent weight is 121 lb. What are the direction and magnitude of the elevator's...
-
In each part, determine the translation equations that will put the quadric in standard position, and find the equation of the quadric in the translated coordinate system. Name the quadric. (a) 9x2 +...
-
Find the number of additions and multiplications required to compute AB if A is an m n matrix and B is an m p matrix.
-
Consider the variation of Gauss-Jordan elimination in which zeros are introduced above and below a leading 1 as soon as it is obtained, and let A be an invertible n n matrix. Show that to solve a...
-
The credit terms 2/10, n/30 are interpreted as: A. 2% cash discount if the amount is paid within 10 days, or the balance due in 30 days. B. 10% cash discount if the amount is paid within 2 days, or...
-
An overstatement of ending inventory in one period results in: A) an understatement of net income for the next period B) no effect on net income for the next period C) an overstatement of the ending...
-
Annie's Fitness sells a set of free weights to a customer for $1,000. The customer pays $600 in cash and puts the rest on her store credit account. Which one of the following statements describes the...
Study smarter with the SolutionInn App