Question

Find the determinant of $\left[\begin{array}{ccc}1^{2}&2^{2}&3^{2}\\2^{2}&3^{2}&4^{2}\\3^{2}&4^{2}&5^{2}\end{array}\right]$

Answer 1

Answer:

$\text {Determinant = } -8$

Step-by-step explanation:

$\text{Find the determinant of} \left[\begin{array}{ccc}1^{2}&2^{2}&3^{2}\\2^{2}&3^{2}&4^{2}\\3^{2}&4^{2}&5^{2}\end{array}\right]$

$\text {Determinant = } 1^2 \times \left|\begin{array}{ccc}3^2&4^2\\4^2&5^2\end{array}\right| - 2^2 \times \left|\begin{array}{ccc}2^2&4^2\\3^2&5^2\end{array}\right| + 3^2\times \left|\begin{array}{ccc}2^2&3^2\\3^2&4^2\end{array}\right|$

$\text {Determinant = } 1^2((3^2)(5^2) - (4^2)(4^2)) - 2^2((2^2)(5^2) - (4^2)(3^2)) + 3^2((2^2)(4^2) - (3^2)(3^2))$

$\text {Determinant = } 1((9)(25) - (16)(16)) - 4((4)(25) - (16)(9)) + 9((4)(16) - (9)(9))$

$\text {Determinant = } -31 + 176 - 153$

$\text {Determinant = } -8$