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A sparse matrix is a two-dimensional data object consisting of m rows and n columns, with a total of m x n values. It is used for storage and computing time as it has fewer non-zero elements than zeros, reducing memory usage. Representing a sparse matrix by a 2D array can lead to memory wastage, so non-zero elements are stored with triples (Row, Column, value). Two common representations for sparse matrix representations are array representation and linked list representation. Arrays represent a sparse matrix with three rows, while linked lists have four fields for each node. Both methods save memory and time by logically designing data structures that traverse only non-zero elements.

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