We want to find the values of a, b, c, and d such that the given matrix product is equal to a 2x2 identity matrix. We will solve a system of equations to find:
<h3>
Presenting the equation:</h3>
Basically, we want to solve:
![\left[\begin{array}{cc}-1&2\\a&1\end{array}\right]*\left[\begin{array}{cc}b&c\\1&d\end{array}\right] = \left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%262%5C%5Ca%261%5Cend%7Barray%7D%5Cright%5D%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Db%26c%5C%5C1%26d%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
The matrix product will be:
![\left[\begin{array}{cc}-b + 2&-c + 2d\\a*b + 1&a*c + d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-b%20%2B%202%26-c%20%2B%202d%5C%5Ca%2Ab%20%2B%201%26a%2Ac%20%2B%20d%5Cend%7Barray%7D%5Cright%5D)
Then we must have:
-b + 2 = 1
This means that:
b = 2 - 1 = 1
We also need to have:
a*b + 1 = 0
we know the value of b, so we just have:
a*1 + b = 0
Now the two remaining equations are:
-c + 2d = 0
a*c + d = 1
Replacing the value of a we get:
-c + 2d = 0
-c + d = 1
Isolating c in the first equation we get:
c = 2d
Replacing that in the other equation we get:
-(2d) + d = 1
-d = 1
Then:
c = 2d = 2*(-1) = -2
So the values are:
If you want to learn more about systems of equations, you can read:
brainly.com/question/13729904
Dh/dt = -32t + 24
-32t + 24 = 0 when maximum
32t = 24
t = 24/32
t = 3/4
To find the maximum height just substitute "t" in
h = -16 (9/16) + 24(3/4) + 7
h = -9 + 18 + 7
h = 16ft
Answer:
0
Step-by-step explanation:
Answer:
It would be 4(X + 3)
Step-by-step explanation:
There are 4 Xs and 12 ones, so the equation is 4X + 12 or 4(X + 3).
Answer:
See below
Step-by-step explanation:
Extreme values of a function are found by taking the first derivative of the function and setting it equal to 0. To determine if it's a minimum or maximum, we set the second derivative equal to 0 and determine if its positive or negative respectively.
Let's do 
as an example
By using the power rule where 
, then 
Now set 
and solve for 
:
By plugging our critical points into 
, we can see that our extreme values are located at 
, 
, and 
.
The second derivative would be 
and plugging in our critical points will tell us if they are minimums or maximums.
If 
, it's a minimum, but if 
, it's a maximum.
Since 
then is a local maximum
Since 
, then is a local minimum
Since 
, then is a global minimum
Therefore, the extreme values of are a global minimum of , a local minimum of , and a local maximum of .
Hope this example helped you understand! I've attached a graph to help you visualize the extreme values and where they're located.
