question archive Determine if the columns of the matrix form a linearly independent set
Determine if the columns of the matrix form a linearly independent set
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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 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. 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 more than one solution. Therefore, the columns of A do not form a linearly independent set. 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 only the trivial solution. Therefore, the columns of A form a linearly independent set.
