Determine if the columns of the matrix form a linearly independent set. Justify your answer. 0 - 8 16 3 1 - 14 - 1 -6 1 -5 - 2 ... Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) O A. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A form a linearly independent set. O B. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A do not form a linearly independent set. O C. If A is the given matrix, then the augmented matrix this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A form a linearly independent set. represents the equation Ax = 0. The reduced echelon form of O D. If A is the given matrix, then the augmented matrix this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A do not form a linearly independent set. represents the equation Ax = 0. The reduced echelon form of LO
Determine if the columns of the matrix form a linearly independent set. Justify your answer. 0 - 8 16 3 1 - 14 - 1 -6 1 -5 - 2 ... Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) O A. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A form a linearly independent set. O B. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A do not form a linearly independent set. O C. If A is the given matrix, then the augmented matrix this matrix indicates that Ax =0 has only the trivial solution. Therefore, the columns of A form a linearly independent set. represents the equation Ax = 0. The reduced echelon form of O D. If A is the given matrix, then the augmented matrix this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A do not form a linearly independent set. represents the equation Ax = 0. The reduced echelon form of LO
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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Transcribed Image Text:Determine if the columns of the matrix form a linearly independent set.
Justjfy your answer.
0 - 8
16
3
1
- 14
- 1
- 6
1
- 5
- 2
Seljct the correct choice below and fill in the answer box within your choice.
(Type an integer or simplified fraction for each matrix element.)
A. If A is the given matrix, then the augmented matrix
represents the equation Ax = 0. The reduced echelon form of
this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A form a linearly independent
set.
B. If A is the given matrix, then the augmented matrix
represents the equation Ax = 0. The reduced echelon form of
this matrix indicates that Ax = 0 has more than one solution. Therefore, the columns of A do not form a linearly
independent set.
C. If A is the given matrix, then the augmented matrix
represents the equation Ax = 0. The reduced echelon form of
this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A form a linearly independent set.
O D. If A is the given matrix, then the augmented matrix
represents the equation Ax = 0. The reduced echelon form of
this matrix indicates that Ax = 0 has only the trivial solution. Therefore, the columns of A do not form a linearly
independent set.
5
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