The value of 12 22 32 22 32 42 32 42 52 is

1^2 amp;2^2 amp;3^2 2^2 amp;3^2 amp;4^2 3^2 amp;4^2 amp;5^2 {Operate R_3 → R_3 R_2, R_2 → R_2 R_1} = 1 amp;4 amp;9 3 amp;5 amp;7 5 a ...

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Properties of Determinants

The value of ...

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The value of $∣ ∣ ∣ ∣ ∣ \begin{matrix} 1^{2} & 2^{2} & 3^{2} 2^{2} & 3^{2} & 4^{2} 3^{2} & 4^{2} & 5^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$ is

-8

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400

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△= ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1^{2} & 2^{2} & 3^{2} 2^{2} & 3^{2} & 4^{2} 3^{2} & 4^{2} & 5^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

A = ⎡ ⎢ ⎣ \begin{matrix} 1^{2} & 2^{2} & 3^{2} 2^{2} & 3^{2} & 4^{2} 3^{2} & 4^{2} & 5^{2} \end{matrix} ⎤ ⎥ ⎦

| A d j A | =

A B C

y

x

z

y

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