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
Answer:
First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)
To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0 x=-4 x=2
So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)
And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5
3 gets us 21
So now you know end behavior, zeroes, and signs of intervals
Hope this helps
90 degree angle witch is Obtuse angle
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Answer:6 songs
Step-by-step explanation:
