Question

$D=\left|\begin{array}{ccc}18& 40& 89\\ 40& 89& 198\\ 89& 198& 440\end{array}\right|=$

• A. $1$
• B. $-1$
• C. zero
• D. $2$

Answer 1

The correct option is B $-1$

We have,

$D=\left|\begin{array}{ccc}18& 40& 89\\ 40& 89& 198\\ 89& 198& 440\end{array}\right|$

$D=18\times (89\times 440-{198}^2)-40\times (40\times 440-198\times 89)+89\times (40\times 198-{89}^2)$

$D=18\times (39160-39204)-40\times (17600-17622)+89\times (7920-7921)$

$D=18\times (-44)-40\times (-22)+89\times (-1)$

$D=-792+880-89$

$D=-1$

Therefore, the value of the determinant is $-1$.