The matrix = ≤ft[ {*20c &0&3&7\\ 2&5&1&3\\ 0&0&2&4\\ 0&0&0&} ] has $\det (\mathrm{A})=100$ and $\mathrm{trace}(\mathrm{A})=14$.

The value of $|a-b|$ is ________.

Calculation:

Given:

Trace (A) = 14, det(A) = 100

Trace of (A) = sum of diagonal elements

≤ft[ {*20c a&0&3&7\\ 2&5&1&3\\ 0&0&2&4\\ 0&0&0&b } ]

14 = a + 5 + 2 + b

a + b = 7 ---(1)

Now,

≤ft( A ) = 5≤ft| {*20c a&3&7\\ 0&2&4\\ 0&0&b } |

$5\times 2\times a\times b=100$

ab = 10 ---(2)

from equation (1) and (2)

Either, a = 5, b = 2

Or, a = 2, b = 5

So,

|a - b| = |5 - 2| = |2 - 5| = 3