Answer:

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:

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)

Operating Rearranging

Factoring

Solving, we have the eigenvalues

$11.25 because 10 times 1.125 is equal to 11.25
<u>ANSWER:
</u>
The total cost of the skate board is $74.61.
<u>SOLUTION:
</u>
Given, Luis wants to buy a skateboard that usually sells for $79.99. all merchandise is discounted by 12%. luis has to pay a state sales tax of 6.75%.
We need to find what is the total cost of the skateboard.
Final cost is nothing but original amount subtracted by discount and added with tax.
final cost = original cost – discount + sales tax
Original cost = $79.99
Discount = 12% of original cost

discount is $9.6 approximately
Sales tax = 6% of cost after discounting

Sales tax is $4.22 approximately
Now, final cost = 79.99 – 9.6 + 4.22
= 84.21 - 9.6
= 74.61
Hence, the total cost of the skate board is $74.61
Answer:

Step-by-step explanation:
<em>First, multiply by exponent rule.</em>
<em>
</em>
<em>
</em>
<em>Then, multiply by the numbers from left to right.</em>
<em>
</em>
<em>
, </em><em>is the correct answer. </em>
Answer:
R = 13%
Step-by-step explanation:
P = $4000
I = $780
T = 18 months = 18/12 years
