Question

What is the probability that a 3*3 matrix with 4 entries as 1 and other as 0 is a non singular matrix????

Answer 1

$\underline{\underline{\Huge\mathfrak{Answer ;}}}$

Dear ,

First consider the number of non-singular matrices with 3 entries being 1 and the rest 0.

They must have one 1 in each of the rows and columns, so the only possibilities are:

^ See the attached File ^

For each of these 6 possibilities we can make any one of the remaining six 0's into a 1. These are all distinguishable. So there are a total of 6×6=36 non-singular 3×3 matrices with 4entries being 1 and the remaining 5 entries 0.

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@dmohit432

Answer 2

hey

here is answer

let the number of non-singular matrices with 3 entries be 1 and the rest be  0.

For each of there are 6 possibilities we can make any one of the remaining six 0's into a 1.

These are all distinguishable.

So there are a total of 6×6=36 non-singular

 3×3 matrices with 4entries be  1 and the remaining 5 entries 0.

hope it helps

thanks