Consider the following. A = O The matrix 1 1 -5 0 2 1 -1 6 To determine whether b is in col(A), which of the following must be true? O The augmented matrix is consistent as a linear system. O The augmented matrix O The matrix Is b in col(A)? O Yes O No A b 1 , b = b Consider the following 1 A b b] is inconsistent as a linear system. can be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row. cannot be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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Question
Consider the following.
A =
O The matrix
To determine whether b is in col(A), which of the following must be true?
O The augmented matrix
is consistent as a linear system.
O The matrix
O The augmented matrix A b
Is b in col(A)?
O Yes
O No
1
1 -5
0
2
1 -1 6
A =
Consider the following.
O The matrix
A
b
O The matrix
b
Is w in row(A)?
O Yes
O No
1
6
To determine whether w is in row(A), which of the following must be true?
O The augmented matrix A W is consistent as a linear system.
1 , b =
1
0 2
1 -1
A
O The augmented matrix
W
A
W
can be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row.
1
b] is inconsistent as a linear system.
cannot be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row.
1 -5
1 , W =
-9]
2 4 -9
[Aw] is inconsistent as a linear system.
А
can be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row.
cannot be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row.
Transcribed Image Text:Consider the following. A = O The matrix To determine whether b is in col(A), which of the following must be true? O The augmented matrix is consistent as a linear system. O The matrix O The augmented matrix A b Is b in col(A)? O Yes O No 1 1 -5 0 2 1 -1 6 A = Consider the following. O The matrix A b O The matrix b Is w in row(A)? O Yes O No 1 6 To determine whether w is in row(A), which of the following must be true? O The augmented matrix A W is consistent as a linear system. 1 , b = 1 0 2 1 -1 A O The augmented matrix W A W can be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row. 1 b] is inconsistent as a linear system. cannot be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row. 1 -5 1 , W = -9] 2 4 -9 [Aw] is inconsistent as a linear system. А can be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row. cannot be row-reduced to a matrix whose last row is zero by operations excluding row interchanges involving the last row.
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