Question

Find minimum number of zeros in a diagonal matrix of order 6.​

Answer 1

• For any triangular matrix of order n, the minimum number of zeros is n(n-1)/2
• It is given that the triangular matrix is of order 6.
• So, the value of n is 6.
• Thereore, we have.
• Minimum number of zeros
• = 6(6-1)/2
• = (6 x 5)/2
• = 3 x 5
• = 15.

Answer 2

The diagonal matrix can have 15 zeros

Given

• diagonal matrix
• order 6.

To find

• The minimum number of zeros in a diagonal matrix

Solution

we are provided with a diagonal matrix with order of 6 and are asked to find the number of zeros that the diagonal matrix can have.

we know that, foreign general definition of diagonal Matrix we can state that a diagonal matrix is a square Matrix where all the elements apart from the diagonal elements are non zero, the diagonal elements can also be zero but there is a condition that anyone of the diagonal elements should be non zero.

we are given that the order of the square matrix is 6,

Therefore the number of zeros that a diagonal matrix can half his given by the standard formula,

n(n-1)/2 where n is the order of the matrix

Therefore, for the given condition where n = 6

the number of zeros the matrix can have would be,

6(6-1)/2

or, 6(5)/2

or, 3×5

or, 15

Therefore, the diagonal matrix can have 15 zeros