ON/MN=NP/NQ
ON/12=15/20
ON=(12*15)/20
ON=9
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
Answer:
this is what i found
Factor
x out of x 2
. x
⋅ x
− 6
x Factor x out of −
6
x
. x
⋅
x +
x
⋅
−
6 Factor x out of x
⋅
x +
x
⋅
−
6
.
x
(
x
−
6 )
Answer:100
Step-by-step explanation:
Expand
x = 150 - 0.5x
Add 0.5x to both sides
x + 0.5x = 150
Simplify x + 0.5x to 1.5x
1.5x = 150
Divide both sides by 1.5
x = 150/1.5
Simplify 150/1.5 to 100
x = 100
What you need to know for this case is that the sum of the internal angles of a triangle is 180 °
We then have the following equation that is given by:
(2x) + (3x) + (4x) = 180
Clearing x we have:
9x = 180
x = 180/9
x = 20
Therefore we have:
m∠A = (40) °
m∠B = (60) °
m∠C = (80) °
Answer:
B) m∠B = 60 °
