Answer:
Verified!
Step-by-step explanation:
Upper or lower triangular matrix does not make any difference in finding eigenvalues because equalizing determinant to zero will lead to the same result.
Let's apply it for 2x2 matix:
![A = \left[\begin{array}{ccc}a&0\\b&c\end{array}\right]\\\\\lambda I - A = \left[\begin{array}{ccc}\lambda&0\\0&\lambda\end{array}\right]-\left[\begin{array}{ccc}a&0\\b&c\end{array}\right]\\\\det(\lambda I - A) = det\left[\begin{array}{ccc}\lambda-a&0\\-b&\lambda-c\end{array}\right]=(\lambda-a)(\lambda-c)=0](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%260%5C%5Cb%26c%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Clambda%20I%20-%20A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Clambda%260%5C%5C0%26%5Clambda%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%260%5C%5Cb%26c%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5Cdet%28%5Clambda%20I%20-%20A%29%20%3D%20det%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Clambda-a%260%5C%5C-b%26%5Clambda-c%5Cend%7Barray%7D%5Cright%5D%3D%28%5Clambda-a%29%28%5Clambda-c%29%3D0)
So, eigenvalues are entries on the diagonal because zeros in upper side or lower side vanishes the remaining part and only we have 
.
So, eigenvalues are 
Let's apply it for 3x3 matrix:
![A = \left[\begin{array}{ccc}a&0&0\\b&c&0\\d&e&f\end{array}\right]\\\\\lambda I - A = \left[\begin{array}{ccc}\lambda&0&0\\0&\lambda&0\\0&0&\lambda\end{array}\right]-\left[\begin{array}{ccc}a&0&0\\b&c&0\\d&e&f\end{array}\right]\\\\det(\lambda I - A) = det\left[\begin{array}{ccc}\lambda-a&0&0\\-b&\lambda-c&0\\-d&-e&\lambda-f\end{array}\right]=(\lambda-a)(\lambda-c)(\lambda-f)=0](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%260%260%5C%5Cb%26c%260%5C%5Cd%26e%26f%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Clambda%20I%20-%20A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Clambda%260%260%5C%5C0%26%5Clambda%260%5C%5C0%260%26%5Clambda%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%260%260%5C%5Cb%26c%260%5C%5Cd%26e%26f%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5Cdet%28%5Clambda%20I%20-%20A%29%20%3D%20det%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Clambda-a%260%260%5C%5C-b%26%5Clambda-c%260%5C%5C-d%26-e%26%5Clambda-f%5Cend%7Barray%7D%5Cright%5D%3D%28%5Clambda-a%29%28%5Clambda-c%29%28%5Clambda-f%29%3D0)
So as above, eigenvalues are entries on the diagonal because zeros in upper side or lower side vanishes the remaining part and only we have 
.
So eigenvalues are 
<u>An</u><u>swer</u><u>:</u>
Given fraction is 6/9 .
→What does fractions in simplest form means?
- Fractions are said to be in simplest form if the HCF of numerator and denominator is equal to 1 .
→ How to convert?
- We will find the HCF of numerator and denominator and we will divide the numerator and denominator by that number.
Now HCF of 6 and 9 is 3.
→ 6/9 = 6÷3/9÷3 = 2/3.
<u>He</u><u>nce</u><u> the</u><u> required</u><u> answer</u><u> is</u><u> </u><u>2</u><u>/</u><u>3</u><u>.</u>
Yes, I do. They are making large transactions without knowing if they will invest anything, and yes, while it is sometimes necessary to take risks, they are not thinking enough about the future and how if they make another mistake everything could go downhill. They also live in the lap of luxury, not cutting out a bit of the money which they w=could be using to repay the debts they owe.
Answer:
8/9
Step-by-step explanation:
x = 0.8888....
10x = 8.88888
10x - x
8.888888.. - 0.88888....
the repeating decimals cancel out
9x = 8
x = 8/9
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
