Evaluate the determinants- beginvmatrix 2 -1 -2 10 - 2 -11138-5 - 0lendvmatrix

Let A= 2 amp; 2 amp; 2 0 amp; 2 amp; 1 3 amp; 5 amp; 0 By expanding along R_2 (second row), we get |A|=0 1 amp; 2 5 amp;0 ...

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Evaluate the determinants.

$∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & - 2 0 & 2 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

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Evaluate the determinants..

$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 1 & - 2 0 & 0 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 4 & 5 1 & 1 & - 2 2 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 0 & 1 & 2 - 1 & 0 & - 3 - 2 & 3 & 0 \end{matrix} ∣ ∣ ∣ ∣$

$∣ ∣ ∣ ∣ \begin{matrix} 2 & - 1 & - 2 0 & 2 & - 1 3 & - 5 & 0 \end{matrix} ∣ ∣ ∣ ∣$

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$∣ ∣ ∣ ∣ \begin{matrix} 3 & - 4 & 5 1 & 1 & - 2 2 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣$

Evaluate the determinants.

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Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & a & a^{2} a & a^{2} & 1 a^{2} & 1 & a \end{matrix} ∣ ∣ ∣ ∣ ∣ = - 4

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{3} - 1 & 0 & a - a^{4} 0 & a - a^{4} & a^{3} - 1 a - a^{4} & a^{3} - 1 & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣ .

Evaluate the determinants.

$[\begin{matrix} 2 & 4 - 5 & - 1 \end{matrix}]$

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