Question

If $A=\left[\begin{array}{ccc}{1}^2& 2^2& 3^2\\ 2^2& 3^2& 4^2\\ 3^2& 4^2& 5^2\end{array}\right]$, then the minor of $a_{22}$ is

• A. $-56$
• B. $51$
• C. $-43$
• D. $41$

Answer 1

Answer: (A)

$-56$

Given, $A=\left[\begin{array}{ccc}{1}^2& 2^2& 3^2\\ 2^2& 3^2& 4^2\\ 3^2& 4^2& 5^2\end{array}\right]$
So, By property of minor (1),
minor of $a_{22}=M_{22}(-1{)}^{2+2}=M_{22}$
$=\left|\begin{array}{cc}{1}^2& 3^2\\ 3^2& 5^2\end{array}\right|$
$=25-9\times 9$
$=-56$