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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.) A. If A is the given matrix, then the augmented matrix B. If A is the given matrix, then the augmented matrix OC. If A is the given matrix, then the augmented matrix 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. 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. 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 solution. Therefore, the columns of A form a linearly independent set. -2-1 0 0 -1 3 1 1 -6 2 1-12

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.) A. If A is the given matrix, then the augmented matrix B. If A is the given matrix, then the augmented matrix OC. If A is the given matrix, then the augmented matrix 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. 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. 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 solution. Therefore, the columns of A form a linearly independent set. -2-1 0 0 -1 3 1 1 -6 2 1-12

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 78E
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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.) A. If A is the given matrix, then the augmented matrix B. If A is the given matrix, then the augmented matrix OC. If A is the given matrix, then the augmented matrix 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. 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. 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 solution. Therefore, the columns of A form a linearly independent set. -2-1 0 0 -1 3 1 1 -6 2 1-12
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.) A. If A is the given matrix, then the augmented matrix B. If A is the given matrix, then the augmented matrix OC. If A is the given matrix, then the augmented matrix 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. 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. 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 solution. Therefore, the columns of A form a linearly independent set. -2-1 0 0 -1 3 1 1 -6 2 1-12
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