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etermine if the columns of the matrix form a linearly independent set. ustify your answer. 2 elect the correct choice below and fill in the answer box within your choice. ype 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 only the trivi solution. Therefore, the columns of A do not form a linearly independent set. OB. 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 trivi solution. Therefore, the columns of A form a linearly independent set.

etermine if the columns of the matrix form a linearly independent set. ustify your answer. 2 elect the correct choice below and fill in the answer box within your choice. ype 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 only the trivi solution. Therefore, the columns of A do not form a linearly independent set. OB. 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 trivi solution. Therefore, the columns of A form a linearly independent set.

Advanced Engineering Mathematics
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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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.) C -2 -1 0 0 6 1 - 12 1 -24 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 do not form a linearly independent set. OB. If A is the given matrix, then the augmented matrix solution. Therefore, the columns of A form a linearly O C. 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. 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. represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial independent set.
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.) C -2 -1 0 0 6 1 - 12 1 -24 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 do not form a linearly independent set. OB. If A is the given matrix, then the augmented matrix solution. Therefore, the columns of A form a linearly O C. 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. 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. represents the equation Ax = 0. The reduced echelon form of this matrix indicates that Ax = 0 has only the trivial independent set.
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