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Evaluate the determinant of the matrix.$\begin{vmatrix}5&2\\7&3\end{vmatrix}=$|5 27 3|=​

Question

Evaluate the determinant of the matrix.

egin{vmatrix}5 & 2 \ 7 & 3
ext{end{vmatrix} = |5 \ 27 \ 3| =

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Solution

The determinant of a 2x2 matrix is calculated as follows:

For the matrix abcd\begin{vmatrix}a&b\\c&d\end{vmatrix}, the determinant is calculated as adbcad - bc.

So, for the matrix 5273\begin{vmatrix}5&2\\7&3\end{vmatrix}, the determinant would be calculated as:

5327=1514=15*3 - 2*7 = 15 - 14 = 1.

So, the determinant of the matrix 5273\begin{vmatrix}5&2\\7&3\end{vmatrix} is 1.

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1/2

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