7. (a) (5 points) Use the properties of determinant to prove that a b c b c a c a b = (a + b + c)(ab + bc + ca − a 2 − b 2 − c 2 ). (b) (4 points) Use the result in part (a) to calculate the volume of parallelepiped with adjacent edges represented by the vectors u = (2, 3, 5), v = (3, 5, 2), and w = (5, 2, 3). (Your solution should clearly reflect the use of part (a), to receive any credit.)

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

step-by-step explanation:

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.