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
Answer:
100.3 units²
Step-by-step explanation:
✅Find the area of the parallelogram:
Area of Parallelogram is given as base × height
base = 10
height = 5
Area of Parallelogram = 10*5 = 50
✅Next, find the area of the two semicircles:
The two semicircles = 1 circle
Area of circle = πr²
r = 8/2 = 4
Area = π*4² = 16π = 50.3 (nearest tenth)
✅Area of figure = 50 + 50.3 = 100.3 units²
Answer:
there is no solution 64x-16=64x-16
Step-by-step explanation:
if you distrubute then you will see the numbers are the same on both sides
Answer:
5/4
Step-by-step explanation:
If the equation is
then the slope is the number multiplying x, so
slope = 5/4.
Hello,
I hope so far you and your family are staying safe and healthy!
We need to solve this step by step.
The college student has $700 in their account. But then she spends $165 on books from that money. So we need to Subtract that.
700 - 165 =535
However, later on, she deposits $190 to the same account. So we need to take the remain we had and add it to the new amount.
535 + 190 = 725
Thus,
There are $725 in the account.
I wish you all the best!
~Gary
