6. Find the inverse of the matrix C where $$ C = begin{bmatrix} a & a &...

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6. Find the inverse of the matrix C where

$$

C =

\begin{bmatrix}

a₁ & a₂ & a₂ & a₂ \\

a₂ & a₃ & a₄ & a₄ \\

a₂ & a₄ & a₃ & a₄ \\

a₂ & a₄ & a₄ & a₃

\end{bmatrix}

$$

if the ai are such that the inverse exists.

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