16x + 64
Hope this helps:)
Answer:
![\lambda=8,\ \lambda=-5](https://tex.z-dn.net/?f=%5Clambda%3D8%2C%5C%20%5Clambda%3D-5)
Step-by-step explanation:
<u>Eigenvalues of a Matrix</u>
Given a matrix A, the eigenvalues of A, called
are scalars who comply with the relation:
![det(A-\lambda I)=0](https://tex.z-dn.net/?f=det%28A-%5Clambda%20I%29%3D0)
Where I is the identity matrix
![I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=I%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
The matrix is given as
![A=\left[\begin{array}{cc}3&5\\8&0\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%265%5C%5C8%260%5Cend%7Barray%7D%5Cright%5D)
Set up the equation to solve
![det\left(\left[\begin{array}{cc}3&5\\8&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda \end{array}\right]\right)=0](https://tex.z-dn.net/?f=det%5Cleft%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%265%5C%5C8%260%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%260%5C%5C0%26%5Clambda%20%5Cend%7Barray%7D%5Cright%5D%5Cright%29%3D0)
Expanding the determinant
![det\left(\left[\begin{array}{cc}3-\lambda&5\\8&-\lambda\end{array}\right]\right)=0](https://tex.z-dn.net/?f=det%5Cleft%28%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3-%5Clambda%265%5C%5C8%26-%5Clambda%5Cend%7Barray%7D%5Cright%5D%5Cright%29%3D0)
![(3-\lambda)(-\lambda)-40=0](https://tex.z-dn.net/?f=%283-%5Clambda%29%28-%5Clambda%29-40%3D0)
Operating Rearranging
![\lambda^2-3\lambda-40=0](https://tex.z-dn.net/?f=%5Clambda%5E2-3%5Clambda-40%3D0)
Factoring
![(\lambda-8)(\lambda+5)=0](https://tex.z-dn.net/?f=%28%5Clambda-8%29%28%5Clambda%2B5%29%3D0)
Solving, we have the eigenvalues
![\boxed{\lambda=8,\ \lambda=-5}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Clambda%3D8%2C%5C%20%5Clambda%3D-5%7D)
Answer:
slope that is undefined
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = A(- 3, 5) and (x₂, y₂ ) = B(- 3, 3)
m =
= ![\frac{-2}{0}](https://tex.z-dn.net/?f=%5Cfrac%7B-2%7D%7B0%7D)
Division by zero is undefined
Thus the slope of AB is undefined
Answer:
x=11 (read below)
Step-by-step explanation:
7 + x = 18
<em>Subtract 7 from both sides</em>
x=11
It's quite simple because if you do something to one side of the equation, you need to do it to the other because otherwise the equation won't be equal. This is how you need to simplify most problems, by taking something from one side and taking from the other as well.
Answer:
No
Step-by-step explanation
8 oz per cup meaning 40oz in 5 paper cups
6 oz per paper cup meaning 36 oz in 6 paper cups