Suppose the weights (in grams) and lengths (in centimeters) of three groups of laboratory animals are given by matrix A, where column 1 gives the lengths and each row corresponds to one group.
If the increase in both weight and length over the next two weeks is 19% for group I, 9% for group II, and 3% for group III, then the increases in the measures during the 2 weeks can be found by computing GA, where
What are the increases in respective weights and measures at the end of these 2 weeks?

Question

Suppose the weights (in grams) and lengths (in centimeters) of three groups of laboratory animals are given by matrix A, where column 1 gives the lengths and each row corresponds to one group. ​
​  ​If the increase in both weight and length over the next two weeks is 19% for group I, 9% for group II, and 3% for group III, then the increases in the measures during the 2 weeks can be found by computing GA, where
​  What are the increases in respective weights and measures at the end of these 2 weeks?
​

Quizplus · Accepted Answer

To find the increases in weight and length, we need to compute GA, where G is a diagonal matrix with the percentage increase for each group on the main diagonal, and A is the original matrix of weights and lengths.

First, we convert the percentage increases to decimal form: 
- Group I: 19% = 0.19 
- Group II: 9% = 0.09 
- Group III: 3% = 0.03

Then, we construct the diagonal matrix G: 
```
G = [1.19   0     0
       0   1.09   0
       0     0   1.03]
```

Finally, we compute GA: 
```
GA = G*A = [362.50   375.00   387.50
               92.40    94.50    96.60
              125.43   129.00   132.57]
```
The first row of GA gives the weights after the increase, and the second row gives the lengths after the increase. To find the increase in weight and length, we subtract the original values from the new values: 
- Group I: weight increase = 387.50 - 375.00 = 12.50 g, length increase = 96.60 - 92.40 = 4.20 cm 
- Group II: weight increase = 94.50 - 92.40 = 2.10 g, length increase = 125.43 - 129.00 = -3.57 cm (note that there was a decrease in length) 
- Group III: weight increase = 132.57 - 129.00 = 3.57 g, length increase = 362.50 - 350.00 = 12.50 cm

Therefore, the answer is C: 
11eb0d3b_97d9_6368_9790_c7a617589560_TB1243_00

Suppose the Weights (In Grams) and Lengths (In Centimeters) of Three