Determine if b is a linear combination of the vectors formed from the columns of the matrix A. A = 0 -3-5 13 7 2,b= -5 7 4-12 19 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. O B. 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. O C. 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 [a b] O 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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 45E
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Determine if b is a linear combination of the vectors formed from the columns of the matrix A.
1
-3-5
7 2
A = 0
4-12 19
b=
13
-5
7
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.
O B. 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.
OC. 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 [a b]
O 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. 1 -3-5 7 2 A = 0 4-12 19 b= 13 -5 7 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. O B. 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. OC. 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 [a b] O 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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