Basis maths-linear algebra-Q9

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An elementary product of a square matrix is any product of its entries with exactly one entry from every row and every column. The number of elementary products in a 5 \times 5 matrix is ___?

asked May 15 in Basic Maths by gbeditor (44,500 points)
reshown May 16 by gbeditor

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a b c d e
f g h i j
k l m n o
p q r s t
u v w x y

Here, agmsy is one elementary product. Similarly, agmtx, fbmsy are elementary products as they contain exactly one entry from each row and each column. So, We can say that for any n x n matrix there will be n! elementary products. 

Elementry product will have 5 elements. For first element we have 5 choices (any of the elements from first column) then for second element we have 4 choices (we can't take the value from the row that first element of the product comes) and so on. Hence, 5 \times 4 \times 3 \times 2 \times 1


answered May 16 by deepak-gatebook (112,390 points)