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Let = | {matrix}a_{11} & a_{12} & a_{13}_{21} &a_{22} &a_{

Question

Let $Δ = ∣ ∣ a_{11} a_{21} a_{31} a_{12} a_{22} a_{32} a_{13} a_{23} a_{33} ∣ ∣$ and $a_{pq} = i^{p + q}$ where $i = - 1 .$ The value of $Δ$ is

real and positive

real and negative

0

imaginary

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Chloe Discussed

Let

Δ = ∣ ∣ a_{11} a_{21} a_{31} a_{12} a_{22} a_{32} a_{13} a_{23} a_{33} ∣ ∣

and

a_{pq} = i^{p + q}

where

i = - 1 .

The value of

Δ

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Text solutionVerified

△ = ∣ ∣ a_{11} a_{21} a_{31} a_{12} a_{22} a_{32} a_{13} a_{23} a_{33} ∣ ∣ & a_{pq} = i^{p + q}

\Rightarrow △ = ∣ ∣ i^{2} i^{3} i^{4} i^{3} i^{4} i^{5} i^{4} i^{5} i^{6} ∣ ∣ = i^{2 + 3 + 4} ∣ ∣ 1 i i^{2} 1 i i^{2} 1 i i^{2} ∣ ∣

= i ∣ ∣ 1 i - 1 1 i - 1 1 i - 1 ∣ ∣ = - i ∣ ∣ 1 i 1 1 i 1 1 i 1 ∣ ∣

∴ △ = 0

Hence, option 'C' is correct.

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Question Text	Let $Δ = ∣ ∣ a_{11} a_{21} a_{31} a_{12} a_{22} a_{32} a_{13} a_{23} a_{33} ∣ ∣$ and $a_{pq} = i^{p + q}$ where $i = - 1 .$ The value of $Δ$ is
Answer Type	Text solution:1
Upvotes	150