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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7x9
3 times 9 and 7 times 9.
9+9 and 9+9+9+9+9
Using multiplication 40 times 45 = 1800
They both cannot be
7x9
3 times 9 and 7 times 9.
Oh, what a happy little question! When you have an array for 2 times 9, you can see 2 rows of 9, which equals 18. And when you have an array for 5 times 9, you can see 5 rows of 9, which equals 45. Keep exploring those arrays and you'll create a beautiful landscape of multiplication facts!
The multiplication fact (singular, not plural 'facts') that can be found is 7x9 = 63. Using the arrays, a 2x9 array (2 rows of 9 items) and 5x9 array (5 rows of 9 items) is 63: 2x9 = 18 5x9 = 45 18 + 45 = 63
9+9 and 9+9+9+9+9
7x9 is the multiplication fact that can be found using the arrays 2x9 and 5x9.
Some common multiplication strategies include the Latis Strategy, The Algebra Strategy, and the Stacking Strategy.
10 x 5?
Using multiplication 40 times 45 = 1800
9
They both cannot be
3 times 35 equals 105