Answer:
Explanation:
Given that:
The abundance of three algal species in Lake A is now represented by the vectors:
[97, 84, 43] and [100, 80, 50]
Now if we look at Lake A, the change occurring in the vector of algae species can be determined as:
a = [100 -97, 80 - 84. 50 - 43]
a = [3, -4, 7]
Thus, the magnitude of that change is:
![|a| = \sqrt{(3)^2 +(-4)^2+(7)^2}](https://tex.z-dn.net/?f=%7Ca%7C%20%3D%20%5Csqrt%7B%283%29%5E2%20%2B%28-4%29%5E2%2B%287%29%5E2%7D)
![|a| = \sqrt{9+16+49}](https://tex.z-dn.net/?f=%7Ca%7C%20%3D%20%5Csqrt%7B9%2B16%2B49%7D)
![|a| = \sqrt{74}](https://tex.z-dn.net/?f=%7Ca%7C%20%3D%20%5Csqrt%7B74%7D)
![|a| =8.6 \ mg/mL](https://tex.z-dn.net/?f=%7Ca%7C%20%3D8.6%20%5C%20mg%2FmL)
The abundance of three algal species in Lake B is now represented by the vectors:
[25, 59, 22] and [20, 63, 15]
At Lake B, the change occurring in the vector of algae species can be determined as:
b = [20 -23, 63 - 59. 15 - 22]
b = [-3, -4, -7]
Thus, the magnitude of that change is:
![|b| = \sqrt{(-3)^2 +(4)^2+(-7)^2}](https://tex.z-dn.net/?f=%7Cb%7C%20%3D%20%5Csqrt%7B%28-3%29%5E2%20%2B%284%29%5E2%2B%28-7%29%5E2%7D)
![|b| = \sqrt{9+16+49}](https://tex.z-dn.net/?f=%7Cb%7C%20%3D%20%5Csqrt%7B9%2B16%2B49%7D)
![|b| = \sqrt{74}](https://tex.z-dn.net/?f=%7Cb%7C%20%3D%20%5Csqrt%7B74%7D)
![|b| =8.6 \ mg/mL](https://tex.z-dn.net/?f=%7Cb%7C%20%3D8.6%20%5C%20mg%2FmL)
Hence, for both Lake A and B, the magnitude of change is the same.