Question

Please don't leave half an answer for the points!

Answer 1

Answer:

1. T . . . labeling shown below
2. U
3. R
4. S

Step-by-step explanation:

Matrix multiplication of A(a rows, b columns) and B(b rows, c columns) will result in a product matrix of AB(a rows, c columns). This fact can be used to reduce the number of candidates for each product.

For the given factor tiles, the resulting product dimensions will be ...

  [2, 3]  [3, 2]  [2, 2]   ⇒  Q, R, S

  [2, 3]  [3, 3]  [3, 2]   ⇒   T, U, V

  [3, 3]   ⇒   W

1. For this 2×3 product, candidates are Q and T. The upper left term for the product in Q is (2)(3) +(1)(7) +(0)(8) = 13. The appropriate choice is T.

2. For this 3×3 product, candidates are U and W. The upper left term for the product in U is 9(2) +1(2) +9(5) +5(1) = 18 +2 +45 +5 = 70. The appropriate choice is U.

3. For this 3×2 product, candidates are R and V. The upper left term for the product in R is 1(4) +2(0) +4(1) = 4 +0 +4 = 8. The appropriate choice is R.

4. For this 2×2 product, there is only one candidate: S.