Eigenvalues:
Eigenvalues of a matrix A are all the values of π for the following equation:
d = det (πI-A) = 0
For a 2x2 diagonal matrix:
![\pi I-A=\left[\begin{array}{ccc}\pi-a1&0\\0&\pi-a2\\\end{array}\right] \\](https://tex.z-dn.net/?f=%5Cpi%20I-A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cpi-a1%260%5C%5C0%26%5Cpi-a2%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Now,
d = det (πI-A)
π1-a1=0 and π2-a2=0
a1=π1 and a2=π2
Hence proved that the eigenvalues of a diagonal matrix are given by the entries on the diagonal.
For a 3x3 diagonal matrix:
![\pi I-A=\left[\begin{array}{ccc}\pi-a1&0&0\\0&\pi-a2\\0&0&\pi-a3\end{array}\right] \\](https://tex.z-dn.net/?f=%5Cpi%20I-A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cpi-a1%260%260%5C%5C0%26%5Cpi-a2%5C%5C0%260%26%5Cpi-a3%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Now,
d = det (πI-A)
π1-a1=0 ; π2-a2=0 ; π3-a3=0
a1=π1 ; a2=π2 ; a3=π3
Hence proved that the eigenvalues of a diagonal matrix are given by the entries on the diagonal.
Answer: yes
Step-by-step explanation:
Lol
Simple, all you want to do is subtract. 7-2=5; and denominators are not subtracted thus it would be 5/8. And that is the simplest form already 5/8.
1/4 + 2/9 = 17/36
Hope this helps you
Brainliest would be appreciated!
-AaronWiseIsBae
Answer: yes
Step-by-step explanation: Joshua