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February 20th, 2018, 06:08 AM   #1
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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!
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February 20th, 2018, 06:47 AM   #2
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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
Thanks from topsquark and Country Boy
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February 21st, 2018, 08:23 PM   #3
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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 08:52 PM.
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February 21st, 2018, 08:52 PM   #4
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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)
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