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hannah2718
hannah2718
07.05.2020 • 
Mathematics

Determine if the statement is true or false, and justify your answer. If A is a matrix with more rows than columns, then the columns of A are linearly independent. False. For example, A = 1 −1 2 2 0 0 has more rows than columns but the columns are linearly dependent. False. For example, A = 1 −1 2 −2 0 0 has more rows than columns but the columns are linearly dependent. False. For example, A = 1 2 3 0 0 0 has more rows than columns, but the columns are linearly dependent. True. The echelon form of the matrix will have at least one row of zeroes at the bottom, which means the columns are linearly independent. True. Since there are more rows than columns, Ax = b will have a unique solution for all b, which means the columns of A are linearly independent.

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