The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is????..
please explain using the concept of permutations and combinations or any other if possible..

Asked by shailesh arlekar | 22nd Mar, 2016, 04:37: PM

Expert Answer:

begin mathsize 12px style straight A space 3 cross times 3 space matrix space has space 9 space elements. space
open square brackets table row _ _ _ row _ _ _ row _ _ _ end table close square brackets
Each space element space can space be space either space 0 space or space 1.
Hence comma space 2 space ways space of space filling space the space element space in space first space row space and space first space column.
Similarly comma space every space blank space can space be space filled space in space 2 space ways space left parenthesis 0 space or space 1 right parenthesis
So space by space multiplication space principle space of space counting comma
9 space blanks space can space be space filled space in space 2 cross times 2 cross times 2... space 9 space times equals 2 to the power of 9 space ways.
Hence comma space the space number space of space all space possible space matrices space is space 2 to the power of 9 equals 512. end style

Answered by satyajit samal | 23rd Mar, 2016, 11:10: AM