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In linear algebra, a numerical value associated with a matrix having the same number of rows as columns. It is particularly useful in solving systems of (linear) equations and in the study of vectors. For a two-by-two matrix, the determinant is the product of the upper left and lower right terms minus the product of the lower left and upper right terms. Determinants of larger matrices involve more complicated arithmetic combinations of the terms and are usually solved using a calculator or computer.
This entry comes from Encyclopædia Britannica Concise. For the full entry on determinant, visit Britannica.com.