Question

Determine whether the statements that follow are true or false, and justify your answer.

50.A matrix is called a 0-1 matrix if all of its entries are ones and zeros. True or false: The majority of the 9-1 matrices of size 3X3 have rank 3.

Short answer

The statement, “The majority of the 0-1 matrices of size 3X3 have rank 3.” is false.

Step-by-step solution

Consider the condition

A matrix of order can have the rank 0,1,2, or 3 .

The probability for a matrix of order 3x3 to have a rank of 3 is very less compared to the matrix having the rank of 0,1 or 2.

Conclusion

Hence, the majority of 0-1 matrices of size 3x3 might have rank 3 , but not every time.