Determine if the columns of the matrix form a linearly independent set. Justify your answer. Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) - 2 - 1 0 - 1 0 5 1 - 10 1 - 20 1 2 OA. 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 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 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 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 do not form a linearly independent set.
Determine if the columns of the matrix form a linearly independent set. Justify your answer. Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) - 2 - 1 0 - 1 0 5 1 - 10 1 - 20 1 2 OA. 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 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 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 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 do not 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.
Select the correct choice below and fill in the answer box within your choice.
(Type an integer or simplified fraction for each matrix element.)
- 2
- 1
0 - 1
0
5
1 - 10
1 - 20
1
2
OA. 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 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 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 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 do not form
a linearly independent set.
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