Answer:
we approach the issue by taking note of that a 2 x 2 matrix can either have 1 0r 2 pivot columns. If the matrix has no pivot columns then every entry in the matrix must be zero.
-> if our matrix has two pivot columns then : ![\left(\begin{array}{rr}-&*&0&-\end{array}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Brr%7D-%26%2A%260%26-%5Cend%7Barray%7D%5Cright%29)
-> if our matrix has one pivot column then we have a choice to make. If the first column is pivot column then: ![\left(\begin{array}{rr}-&*&0&0\end{array}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Brr%7D-%26%2A%260%260%5Cend%7Barray%7D%5Cright%29)
->otherwise, if the pivot column is the second column then: ![\left(\begin{array}{rr}0&-&0&0\end{array}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Brr%7D0%26-%260%260%5Cend%7Barray%7D%5Cright%29)
Answer:
A
Step-by-step explanation:
The n th term formula for a geometric sequence is
= a![(r)^{n-1}](https://tex.z-dn.net/?f=%28r%29%5E%7Bn-1%7D)
where a is the first term and r the common ratio
here a = - 5 and r = - 10 ÷ - 5 = 2, thus
= - 5(
→ A
soln
given,
f(x) = 1
Now,
f(x) = 4x+11
or, -1 =4x +11
or,4x = 11+1
or, 4x = 12
or, x. =12/4
or x. = 3
Therefore, The value of x is 3.
we know that
The average rate of change of the function f(x) over the interval [a,b] is equal to
![\frac{(f(b)-f(a))}{(b-a)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28f%28b%29-f%28a%29%29%7D%7B%28b-a%29%7D%20%20)
in this problem
![f(x)=17 -x^{2}](https://tex.z-dn.net/?f=%20f%28x%29%3D17%20-x%5E%7B2%7D%20%20%20%20%20)
interval [a,b]---------->![[1,5]](https://tex.z-dn.net/?f=%20%20%5B1%2C5%5D%20)
for ![x=1](https://tex.z-dn.net/?f=%20x%3D1%20)
![f(1)=17 -1^{2} =16](https://tex.z-dn.net/?f=%20f%281%29%3D17%20-1%5E%7B2%7D%20%3D16%20%20%20%20)
for ![x=5](https://tex.z-dn.net/?f=%20x%3D5%20)
![f(5)=17 -5^{2} =-8](https://tex.z-dn.net/?f=%20f%285%29%3D17%20-5%5E%7B2%7D%20%3D-8%20%20%20%20)
substitute the values
![\frac{(f(b)-f(a))}{(b-a)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28f%28b%29-f%28a%29%29%7D%7B%28b-a%29%7D%20%20)
![\frac{(-8-16)}{(5-1)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28-8-16%29%7D%7B%285-1%29%7D%20%20)
![=-6](https://tex.z-dn.net/?f=%20%3D-6%20)
therefore
<u>the answer is</u>
The average rate of change is equal to ![-6](https://tex.z-dn.net/?f=%20-6%20)