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 23E from Chapter 1.1 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 23E
Chapter:
Problem:
In Exercises 23 and 24, key statements from this section are either quoted directly, restated slightly (but still true), or altered in some way that makes them false in some cases....
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: Every elementary row operation is reversible.
The statement is True. For example we can reverse multiplication by multiplying by its inverse.
Therefore,
TRUE
Step 3: (b)
Statement: A $5 \times 6$ matrix has six rows.
The statement is False. A $5 \times 6$ matrix has 5 rows and six columns.
Therefore,
FALSE
Step 4: (c)
Statement: The solution set of a linear system involving variables ${x_1},...{x_n}$ is a list of numbers .${s_1},...{s_n}$ that makes each equation in the system a true statement when the values ${s_1},...{s_n}$ are substituted for ${x_1},...{x_n}$, respectively.
The statement is False. The case is applicable when the system has a single solution, when the system contains many solutions, the statement is not applicable.
Therefore,
FALSE
Step 5: (d)
Statement: Two fundamental questions about a linear system involve existence and uniqueness
The statement is True. The fundamental questions about a linear system are:
(1) Is the system consistence, that is does at least one solution exist
(2) If a solution exists, is it the only one, that is, is the solution unique..
Therefore,
TRUE
We are given with some statements, we have to find whether the given statements re true or False:
Step 2: (a)
Statement: Every elementary row operation is reversible.
The statement is True. For example we can reverse multiplication by multiplying by its inverse.
Therefore,
TRUE
Step 3: (b)
Statement: A $5 \times 6$ matrix has six rows.
The statement is False. A $5 \times 6$ matrix has 5 rows and six columns.
Therefore,
FALSE
Step 4: (c)
Statement: The solution set of a linear system involving variables ${x_1},...{x_n}$ is a list of numbers .${s_1},...{s_n}$ that makes each equation in the system a true statement when the values ${s_1},...{s_n}$ are substituted for ${x_1},...{x_n}$, respectively.
The statement is False. The case is applicable when the system has a single solution, when the system contains many solutions, the statement is not applicable.
Therefore,
FALSE
Step 5: (d)
Statement: Two fundamental questions about a linear system involve existence and uniqueness
The statement is True. The fundamental questions about a linear system are:
(1) Is the system consistence, that is does at least one solution exist
(2) If a solution exists, is it the only one, that is, is the solution unique..
Therefore,
TRUE