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Solve for x:|{:(x,x),(8,x):}| = |{:(7,-2...

Solve for `x:|{:(x,x),(8,x):}| = |{:(7,-2,1),(0,3,-1),(5,-4,2):}|`.

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To solve the equation \( | \begin{pmatrix} x & x \\ 8 & x \end{pmatrix} | = | \begin{pmatrix} 7 & -2 & 1 \\ 0 & 3 & -1 \\ 5 & -4 & 2 \end{pmatrix} | \), we will follow these steps: ### Step 1: Calculate the determinant of the 2x2 matrix The determinant of a 2x2 matrix \( \begin{pmatrix} A & B \\ C & D \end{pmatrix} \) is given by the formula: \[ | \begin{pmatrix} A & B \\ C & D \end{pmatrix} | = AD - BC \] For our matrix \( \begin{pmatrix} x & x \\ 8 & x \end{pmatrix} \), we have: ...
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