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Create random matrices in SageMath

asked 2016-11-02 18:11:04 -0500

kathy reyes gravatar image

updated 2017-01-05 15:13:00 -0500

FrédéricC gravatar image

Create two random 7 × 7 integer matrices A and B. Check whether any of the following identities hold or not: 1. det(AB) = det(A) det(B)

  1. det(A + B) = det(A) + det(B) 3. det(A−1)=1/det(A)

  2. det ([ A 0 ]) = det(A) det(B)(the 0 denote 7 × 7 zero matrices) 0B

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What have you tried? Woudl it be possible for you to post some of your code. Didi you look at this question? Here's some simply code to help you generate a 7 x 7 matrix with some random integers B = matrix(7,7, sample(xrange(100), 49)); B however, I am not sure that this is what you are looking for. If you specific and post code I'll be happy to try to help you!

etb gravatar imageetb ( 2016-11-03 03:39:07 -0500 )edit

Have you tried the random_matrix command?

John Palmieri gravatar imageJohn Palmieri ( 2016-11-03 12:32:52 -0500 )edit
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Are you just copying a homework problem? It looks very much like it. Have you searched the web? Usually adding "sagemath" to your query gives very good results, for instance search [random matrix sagemath].

slelievre gravatar imageslelievre ( 2016-11-04 02:34:17 -0500 )edit

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answered 2016-11-03 12:46:06 -0500

ndomes gravatar image

Define a 7x7 random matrix (you must give the base ring (in my example integer ring (ZZ)):

A = random_matrix(ZZ,7,7)

Zero matrix:

O = zero_matrix(7,7)

or:

O = matrix(7,7,0)

Identity matrix:

E = identity_matrix(7,7)

or:

E = matrix(7,7,1)
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Asked: 2016-11-02 18:10:17 -0500

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Last updated: Nov 04 '16