If - - i- - - - - - - - Find - - i-1

The correct option is B (α + iβ)^ 1 = [ α β; β α ]^ 1 Let A = #160; [ α amp; β; β amp; α ] ∴ A^ 1 = [ α amp; β; β amp ...

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Adjoint of a Matrix

If α + iβ =...

Question

If $α + i β = [\begin{matrix} α & β - β & α \end{matrix}]$ ,

Find $(α + i β)^{- 1}$

(α + i β)^{- 1} = {[\begin{matrix} α & β β & α \end{matrix}]}^{- 1}

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(α + i β)^{- 1} = {[\begin{matrix} α & β - β & α \end{matrix}]}^{- 1}

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(α + i β)^{- 1} = {[\begin{matrix} α & - β β & α \end{matrix}]}^{- 1}

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(α + i β)^{- 1} = {[\begin{matrix} α & - β - β & - α \end{matrix}]}^{- 1}

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Solution

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β

∣ ∣ ∣ \frac{α + i β}{β + i α} ∣ ∣ ∣ =

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= \frac{α + 1}{α - β} + \frac{β + 1}{β - α} = \frac{α - β}{α - β}

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