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What is the determinant of the coefficient matrix of this system?
4x-3y=-8
8x-3y=12

User John F
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1 Answer

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The coefficient matrix is build with its rows representing each equation, and its columns representing each variable.

So, you may write the matrix as


\left[\begin{array}{cc}\text{x-coefficient, 1st equation}&\text{y-coefficient, 1st equation}\\\text{x-coefficient, 2nd equation}&\text{y-coefficient, 2nd equation} \end{array}\right]

which means


\left[\begin{array}{cc}4&-3\\8&-3\end{array}\right]

The determinant is computed subtracting diagonals:


\left | \left[ \begin{array}{cc}a&b\\c&d\end{array}\right]\right | = ad-bc

So, we have


\left | \left[\begin{array}{cc}4&-3\\8&-3\end{array}\right] \right | = 4(-3) - 8(-3) = -4(-3) = 12

User Waltflanagan
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