Question

The number of 3× symmetric matrices with 5 entries are 1 and 4 entries are o is​

Answer 1

Given: Entries in matrices are 5 entries are 1 and 4 entries are 0.

To find: The number of 3 x 3 symmetric matrices.

Solution:

• Now we have given that there are 5 entries are 1 and 4 entries are 0.

• Two cases arises:

• Case 1:

• Diagonal elements are 1, i.e. three elements are 1

• So the number of matrices will be:

                   3C1 = 3

• Case 2:

• One element of diagonal is 1 and rest two elements are zero

• So the number of matrices will be:

                   3C1 x 3C1 = 9

• Now total matrices will be: 3 + 9 = 12

Answer:

           So the number of 3 x 3 symmetric matrices are 12.