Assume we have 1000 data points x1,x2,···,x1000∈r50. we know that thesingular values of the data matrix are given asσ1= 10,σ2= 9,σ3= 8,···,σ10= 1,σ11=0,···. we would like to find a low dimensional representation of the data points in a waythat at least 50% of the energy of the data is kept. what is the minimum value of the dimension that we can use for the low-dimensional representation of the data

the image of (6, 9) under a dilation is (4, 6). the scale factor is

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

he kicked it up? is this the answer ?

step-by-step explanation: