Determine if the columns of the matrix form a linearly independent set. Justify your answer. O -8 3 1 - 14 16 -1 5 -8 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. 1 -5 -20 O 16 -8 0 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 0 - 10 0 independent set. O B. IfA 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. OC. IfA 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 D. IfA 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.
Determine if the columns of the matrix form a linearly independent set. Justify your answer. O -8 3 1 - 14 16 -1 5 -8 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. 1 -5 -20 O 16 -8 0 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 0 - 10 0 independent set. O B. IfA 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. OC. IfA 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 D. IfA 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.
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.
Justify your answer.
0 - 8
16
3
1
- 14
- 1
- 8
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.)
A.
1
- 5
-2 0
16
- 8 0
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
-10 0
0 0
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 only the trivial 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
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 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 more than one solution. Therefore, the columns of A form a linearly independent
set.
LO
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