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Ede4ka [16]
3 years ago
8

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

Mathematics
1 answer:
gladu [14]3 years ago
8 0

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

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