How many invertible 3X3 matrices are there whose entries are 1's and 0's? (Prob. 21 in Sect 2.5)

Question

anonymous · Answer

for the a matrix to be invertable the columns must be lin idependant. which meens there must be a pivot in every column. So i THINK only the indentity will be invertable if you limit you elements to 1s and 0s

anonymous · Answer

i take that back anything that is upper triangular is also invertale because the columns are still lin ind

anonymous · Answer

All permutations of 3x3 identity. It is,3!=6

anonymous · Answer

Identity matrix + upper triangular +lower triangualr permutations
Think frnds. I will come back with answer soon.

anonymous · Answer

Well, I guess the problem is not that easy (if someone found an elegant way, please post it).

I wrote a program which constructs all the 2^9 = 512 possible matrices and checks which of them are actually invertible. The result is: 174 matrices are invertible.

(I attached the script if someone wants to see it.)

datanewb · Answer

I don't speak python, but verbit's script logic seems correct.  Just thought I'd point out that the question in the book was concerning 2x2 matrices, of which there are only 16. :)