What multiplication fact can be found by using arrays for 2 times 9 and 5 times 9?

Answer 1

Assume two matrices are to be multiplied (the generalization to any number is discussed below). Arithmetic process of multiplying numbers (solid lines) in row i in matrix A and column j in matrix B, then adding the terms (dashed lines) to obtain entry ij in the final matrix.

If A is an n × m matrix and B is an m × p matrix, the matrix product AB

where each i, j entry is given by multiplying the entries Aik (across row i of A) by the entries Bkj (down column j of B), for k = 1, 2, ..., m, and summing the results over k:

Thus the product AB is defined only if the number of columns in A is equal to the number of rows in B, in this case m. Each entry may be computed one at a time.

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