Answer:
Entries of I^k are are also identity elements.
Step-by-step explanation:
a) For the 2×2 identity matrix I, show that I² =I
![I^{2}=\left[\begin{array}{cc}1&0\\0&1\end{array}\right] \times \left[\begin{array}{cc}1&0\\0&1\end{array}\right] \\\\=\left[\begin{array}{cc}1\times 1+0\times 0&1\times 0+0\times 1\\0\times 1+1\times 0&0\times 0+1\times1\end{array}\right] \\\\=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=I%5E%7B2%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%5Ctimes%201%2B0%5Ctimes%200%261%5Ctimes%200%2B0%5Ctimes%201%5C%5C0%5Ctimes%201%2B1%5Ctimes%200%260%5Ctimes%200%2B1%5Ctimes1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
Hence proved I² =I
b) For the n×n identity matrix I, show that I² =I
n×n identity matrix is as shown in figure
Elements of identity matrix are
As square of 1 is equal to 1 so for n×n identity matrix I, I² =I
(c) what do you think the enteries of Ik are?
As mentioned above
Any power of 1 is equal to 1 so kth power of 1 is also 1. According to this Ik=I
Filipe can choose his favorite from 4 bands, so he has 4 ways to determine the favorite.
Then only 3 bands left and he can choose his second favorite in 3 ways. After selecting second favorite, only 2 bands left and there are 2 ways to select the third favorite.
Use the product rule to count all possible votes:
4·3·2=24 ways.
Answer: 24.
When one organism gains a benefit at the expense of a second organism and causes them harm is called:
A. Parasitism
B. Mutualism
C. Commensalism
D. Predation
Use the Pythagorean theorem.
The answer is 5
Answer:
Step-by-step explanation:
Given that: x
2
+6x+8
=x
2
+4x+2x+8, (split middle term)
=(x
2
+4x)+(2x+8), (group pair of terms)
=x(x+4)+2(x+4), (factor each binomials)
=(x+4)(x+2), (factor out common factor (x+4)
Hence factors of x
2
+6x+8 are (x+4)(x+2)
