Determine if b is a linear combination of the vectors formed from the columns of the matrix A. Choose the correct answer below. 1 A = 0 4 - 4 5 - 16 - 3 6 11 10 -5 8 O A. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column. B. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. There is no solution to the linear system corresponding to the matrix [Ab ]. C. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column and the second entry in the second column. There are no pivots in the third and fourth columns. D. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are only in the first entry in the first column and the second entry in the second column. There are no pivots in the third and fourth columns.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Determine if b is a linear combination of the vectors formed from the columns of the
matrix A.
Choose the correct answer below.
1
A = 0
4
- 4
5
- 16
- 3
6
11
10
-5
8
O A. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the
corresponding echelon matrix are in the first entry in the first column, the second entry in the second column,
and the third entry in the third column.
B. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. There is no solution
to the linear system corresponding to the matrix [Ab
].
C. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the
corresponding echelon matrix are in the first entry in the first column and the second entry in the second
column. There are no pivots in the third and fourth columns.
D. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. The pivots in the
corresponding echelon matrix are only in the first entry in the first column and the second entry in the second
column. There are no pivots in the third and fourth columns.
Transcribed Image Text:Determine if b is a linear combination of the vectors formed from the columns of the matrix A. Choose the correct answer below. 1 A = 0 4 - 4 5 - 16 - 3 6 11 10 -5 8 O A. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column. B. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. There is no solution to the linear system corresponding to the matrix [Ab ]. C. Vector b is a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are in the first entry in the first column and the second entry in the second column. There are no pivots in the third and fourth columns. D. Vector b is not a linear combination of the vectors formed from the columns of the matrix A. The pivots in the corresponding echelon matrix are only in the first entry in the first column and the second entry in the second column. There are no pivots in the third and fourth columns.
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