Linear Algebra and Its Applications, 5th Edition
Authors: David C. Lay, Steven R. Lay, Judi J. McDonald
ISBN-13: 978-0321982384
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See our solution for Question 24E from Chapter 1.1 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 24E
Chapter:
Problem:
a. Elementary row operations on an augmented matrix never change the solution set of the associated linear system...
Step-by-Step Solution
Given Information
We are given with some statements, we have to find whether the given statements re true or False:
Step 2: (a)
Statement: Elementary row operations on an augmented matrix never change the solution set of the associated linear system
The statement is True by Matrix properties.
Therefore,
TRUE
Step 3: (b)
Statement: Two matrices are row equivalent if they have the same number of rows.
The statement is False. By a sequence of row operations if one matrix can be converted to another matrix, the are called row equivalent.
Therefore,
FALSE
Step 4: (c)
Statement: An inconsistent system has more than one solution.
The statement is False. By definition of inconsistent system, the system should have no solution
Therefore,
FALSE
Step 5: (d)
Statement: Two linear systems are equivalent if they have the same solution set.
The statement is True by definition of equivalent systems. Each solution of the first system is a solution of the second system and vice versa.
Therefore,
TRUE
We are given with some statements, we have to find whether the given statements re true or False:
Step 2: (a)
Statement: Elementary row operations on an augmented matrix never change the solution set of the associated linear system
The statement is True by Matrix properties.
Therefore,
TRUE
Step 3: (b)
Statement: Two matrices are row equivalent if they have the same number of rows.
The statement is False. By a sequence of row operations if one matrix can be converted to another matrix, the are called row equivalent.
Therefore,
FALSE
Step 4: (c)
Statement: An inconsistent system has more than one solution.
The statement is False. By definition of inconsistent system, the system should have no solution
Therefore,
FALSE
Step 5: (d)
Statement: Two linear systems are equivalent if they have the same solution set.
The statement is True by definition of equivalent systems. Each solution of the first system is a solution of the second system and vice versa.
Therefore,
TRUE