Yahoo Answers is shutting down on 4 May 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
How to find the inverse of a diagonal matrix?
Find A^-1 if A =
[alpha, 0, 0]
[0, beta, 0]
[0, 0 , epsilon]
I've looked online and notes that the answer is:
[1/alpha, 0, 0]
[0, 1/beta, 0]
[0, 0, 1/epsilon]
I want to know why. Examples on youtube and my notes do not explain the steps. All they say is that the inverse is 1 over the element.
So whenever I see a diagonal matrix and asked for the inverse, the answer I put down is 1 over the element? I don't have to write any steps to prove that it is because it is stated that it's always 1 over the element.
4 Answers
- zLv 510 years agoFavourite answer
Yes they are right. To verify it, just multiply A and A^(-1) back to see if you get an identity matrix.
- Anonymous6 years ago
This Site Might Help You.
RE:
How to find the inverse of a diagonal matrix?
Find A^-1 if A =
[alpha, 0, 0]
[0, beta, 0]
[0, 0 , epsilon]
I've looked online and notes that the answer is:
[1/alpha, 0, 0]
[0, 1/beta, 0]
[0, 0, 1/epsilon]
I want to know why. Examples on youtube and my notes do not explain the steps. All they say is that the inverse is 1 over...
Source(s): find inverse diagonal matrix: https://biturl.im/hPe5g - Anonymous5 years ago
a = | 2_, -1 | | -1, 2_ | inv a = | 2/3, 1/3 | | 1/3, 2/3 | b = |0 0| |0 0| inverse of 4x4 = [inv a , b ] [b , inv a] = | 2/3, 1/3, 0__, 0__ | | 1/3, 2/3, 0__, 0__ | | 0__, 0__, 2/3, 1/3 | | 0__, 0__, 1/3, 2/3 |
