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Unformatted text preview: independent. What about the rows? 1 2 1 1-1 1 The columns of a matrix are linearly independent if and only if the homogeneous system with the matrix as the coeﬃcients has only the trivial solution. So, we need to solve the system corresponding to the augmented matrix 1 2 0 1 1 0-1 1 0 This matrix is row equivalent to the matrix 1 2 0-1 0 0 0 which represents a system with the unique solution x 1 = 0, x 2 = 0. In particular, the system only has the trivial (all zeros) solution, so the columns are linearly independent. As for the rows of the matrix, they are vectors in ( R ) 2 , and there are three of them, so by a fact stated in class, it is not possible for them all to be linearly independent, so the rows are linearly dependent. 2...
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