Let A=4−2αβ. If A2+γA+18I=0, then detA is equal to

Characteristic equation A-λI=04-λ-2αβ-λ=04−λβ−λ+2α=04β-4+βλ+λ2+2α=0λ2−4+βλ+A=0Now λ=AA2−4+βA+AI =0∴ A=18

Let A=4−2αβ. If A2+γA+18I=0, then detA is equal to

Characteristic equation A-λI=04-λ-2αβ-λ=04−λβ−λ+2α=04β-4+βλ+λ2+2α=0λ2−4+βλ+A=0Now λ=AA2−4+βA+AI =0∴ A=18

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Let $A= [\begin{matrix} 4 & - 2 \\ α & β \end{matrix}]$ . If $A^{2} + γ A + 18 I = 0$ , then detA is equal to

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Characteristic equation $|A- λ I| = 0$

$|\begin{matrix} 4 - λ & - 2 \\ α & β - λ \end{matrix}| = 0$

$(4 - λ) (β - λ) + 2 α = 0$

$4 β - (4 + β) λ + λ^{2} + 2 α = 0$

$λ^{2} - (4 + β) λ + |A| = 0$

Now $λ = A$

$A^{2} - (4 + β) A + |A| I =0$

$∴ |A| =18$

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Let A=4−2αβ. If A2+γA+18I=0, then detA is equal to

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Let $A= [\begin{matrix} 4 & - 2 \\ α & β \end{matrix}]$ . If $A^{2} + γ A + 18 I = 0$ , then detA is equal to