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
Hello!
Since D is the midpoint and the two equations are and both sides of point D the equations equal each other
9x - 7 = 3x + 17
Now you solve it algebraically
Add 7 to both sides
9x = 3x + 24
Subtract 3x from both sides
6x = 24
Divide both sides by 6
x = 4
Now we put this into both equations and add them
9(4) - 7 = 29
3(4) + 17 = 29
29 + 29 = 58
The answer is 58 units
Hope this helps!
Answer:
0
Step-by-step explanation:
Answer:
It's choice 2. c = 3 sin 45 / sin 40.
Step by-step explanation:
m< A = 180 - 45-95
= 180 - 140
= 40 degrees.
So by the Sine Rule:
c / sin 45 = 3 / sin A
Cross multiply:
c sin A = 3 sin 45
c = 3 sin 45 / sin 40.
The total amount of interest earned each year will be
5.2% × $1,500,000 = $78,000
_____
We would need to know more about the beneficiaries (their number and the way they might split the proceeds) and how they might use the balance in the account (whether interest only, or interest and principal are withdrawn) before we could answer the question asked.
