February 20th, 2018, 05:08 AM | #1 |
Newbie Joined: Feb 2018 From: switzerland Posts: 2 Thanks: 0 | Help please!
I am given a 4x4 matrix, M: 5 4 -2 3 5 7 -1 8 5 7 6 10 5 7 1 9 and I'm asked to find a 3x3 matrix A of the form 3 1 5 3 * * 3 * * such that det(M) = 5 det(A) I'm not sure how to start and I really appreciate any help given! Thank you! |
February 20th, 2018, 05:47 AM | #2 |
Global Moderator Joined: Dec 2006 Posts: 18,702 Thanks: 1527 |
As det(M) = 45, you need det(A) to be 9. A possible answer (one of many) is shown below. 3 1 5 3 0 1 3 1 2 |
February 21st, 2018, 07:23 PM | #3 |
Newbie Joined: Feb 2018 From: switzerland Posts: 2 Thanks: 0 |
Hi skipjack, thanks for your reply! However, I was wondering whether there is another way to do this, because the second part of the question requires me to find a 2×2 matrix, 7 2 2 * such that det (A) = 3 det(B) And derive det (M) from det (B). Once again, thank you for your help! Last edited by skipjack; February 21st, 2018 at 07:52 PM. |
February 21st, 2018, 07:52 PM | #4 |
Global Moderator Joined: Dec 2006 Posts: 18,702 Thanks: 1527 |
I doubt that you are expected to find a different approach. The main idea seems to be to check whether you know how to calculate determinants. If B is the 2×2 matrix you have to find, det(B) = det(A)/3 = 9/3 = 3. Hence B is as shown below. 7 2 2 1 det(M) = 5det(A) = 5 × 3det(B) = 15det(B) |