Question

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Answer 1

Answer: -280

Step-by-step explanation:

Given:

$A&=\left[\begin{array}{ccc}1^2&2^2&3^2\\2^2&3^2&4^2\\5^2&4^2&5^2\end{array}\right]$

Simplify it.

$\begin{aligned}A&=\left[\begin{array}{ccc}1^2&2^2&3^2\\2^2&3^2&4^2\\5^2&4^2&5^2\end{array}\right] \\&=\left[\begin{array}{ccc}1&4&9\\4&9&16\\25&16&25\end{array}\right]\end{aligned}$

Find the determinant of $A$.

$\begin{aligned}\left | A \right |&=\left|\begin{array}{ccc}1&4&9\\4&9&16\\25&16&25\end{array}\right|\\&=1\left[(9\times25)-(16\times16)\right]-4\left[(4\times25)-(16\times25)\right]+9\left[(4\times16)-(9\times25)\right]\\&=1\left[225-256 \right ]-4\left[100-400 \right ]+9\left[64-225\right ]\\&=1\left[-31 \right ]-4\left[-300 \right ]+9\left[-161 \right ]\\&=-31+1200-1449\\&=-280\end{aligned}$