Question

write the number of all possible matrices of order 2x2 with each entry 1,2 or 3.

Answer 1

we have find out number of matrices of order 2 × 2 with each entry 1 , 2 or 3.

We know, given n × n matrix with limited m elements , then possible number of matrices will be $\bold{m^{(n^2)}}$

Here number of elements { limited elements } , m = 3 and n = 2
Now , number of matrices =$\bold3^{2\times2}} = \bold{3^4=81}$

Answer 2

According to the counting principle there will be 3 x 3 x 3 x 3 = 81 matrices.

The fundamental counting principle or the counting rule is a way to figure out the number of outcomes in a probability problem. The events are multiplied together to get the total number of outcomes. For example, if there are m ways to do a thing and n ways to do another, then there are m * n ways of doing both. This principle is a guiding rule for finding the number of ways in which two tasks can be accomplished.