Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Determine if the columns of the matrix form a linearly independent set.
Justify your answer.
C
0-8 16
3 1 -14
- 1
5 - 7
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.)
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 more than one
solution. Therefore, the columns of A do not form a linearly independent set.
O B. If A is the given matrix, then the augmented matrix
solution. Therefore, the columns of A form a linearly
represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial
independent set.
represents the equation Ax=0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one
independent set.
O C. IfA is the given matrix, then the augmented matrix
solution. Therefore, the columns of A form a linearly
OD. 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.
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Transcribed Image Text:Determine if the columns of the matrix form a linearly independent set. Justify your answer. C 0-8 16 3 1 -14 - 1 5 - 7 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.) 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 more than one solution. Therefore, the columns of A do not form a linearly independent set. O B. If A is the given matrix, then the augmented matrix solution. Therefore, the columns of A form a linearly represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial independent set. represents the equation Ax=0. The reduced echelon form of this matrix indicates that Ax = 0 has more than one independent set. O C. IfA is the given matrix, then the augmented matrix solution. Therefore, the columns of A form a linearly OD. 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.
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