Evaluate :\(\begin{bmatrix} 1^2& 2^2 & 3^2 \\[0.3em] 2^2 & 2^2 & 4^2 \

1.	Evaluate :\(\begin{bmatrix} 1^2& 2^2 & 3^2 \\[0.3em] 2^2 & 2^2 & 4^2 \\[0.3em] 3^2 &4^2 & 5^2 \end{bmatrix}\)[(1^2,2^2,3^2)(2^2,2^2,4^2)(3^2,4^2,5^2)]
Answer» \(\begin{bmatrix}1^2& 2^2 & 3^2 \\[0.3em]2^2 & 2^2 & 4^2 \\[0.3em]3^2 &4^2 & 5^2\end{bmatrix}\) = \(\begin{bmatrix}1 &4 & 9 \\[0.3em]4 & 9 & 16 \\[0.3em]9 & 16 & 25\end{bmatrix}\) Expanding by first row, we get, 1(9 × 25 - 16 × 16) + 4(16 × 9 - 4 × 25) + 9(4 × 16 - 9 × 9) = - 31 + 176 - 153 =- 8

Evaluate :\(\begin{bmatrix} 1^2& 2^2 & 3^2 \\[0.3em] 2^2 & 2^2 & 4^2 \\[0.3em] 3^2 &4^2 & 5^2 \end{bmatrix}\)[(1^2,2^2,3^2)(2^2,2^2,4^2)(3^2,4^2,5^2)]

Answer»

\(\begin{bmatrix}1^2& 2^2 & 3^2 \\[0.3em]2^2 & 2^2 & 4^2 \\[0.3em]3^2 &4^2 & 5^2\end{bmatrix}\) = \(\begin{bmatrix}1 &4 & 9 \\[0.3em]4 & 9 & 16 \\[0.3em]9 & 16 & 25\end{bmatrix}\)

Expanding by first row, we get,

1(9 × 25 - 16 × 16) + 4(16 × 9 - 4 × 25) + 9(4 × 16 - 9 × 9) = - 31 + 176 - 153 =- 8

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Evaluate :\(\begin{bmatrix} 1^2&amp; 2^2 &amp; 3^2 \\[0.3em] 2^2 &amp; 2^2 &amp; 4^2 \\[0.3em] 3^2 &amp;4^2 &amp; 5^2 \end{bmatrix}\)[(1^2,2^2,3^2)(2^2,2^2,4^2)(3^2,4^2,5^2)]

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Evaluate :\(\begin{bmatrix} 1^2& 2^2 & 3^2 \\[0.3em] 2^2 & 2^2 & 4^2 \\[0.3em] 3^2 &4^2 & 5^2 \end{bmatrix}\)[(1^2,2^2,3^2)(2^2,2^2,4^2)(3^2,4^2,5^2)]