Evaluate the determinant.
$| \begin{array}{ll} - 2 & 2 \\ - 6 & 5 \end{array} |$
The determinant is (Simplify your answer.)

Answer

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Answer

Final Answer: The determinant of the given matrix is $2$

Steps

Step 1 ：We are given a 2x2 matrix and asked to evaluate its determinant. The matrix is $| \begin{array}{ll} - 2 & 2 \\ - 6 & 5 \end{array} |$

Step 2 ：The determinant of a 2x2 matrix $| \begin{array}{ll} a & b \\ c & d \end{array} |$ is given by the formula ad - bc.

Step 3 ：In this case, a = -2, b = 2, c = -6, and d = 5.

Step 4 ：So, we need to calculate (-2*5) - (2*-6).

Step 5 ：By performing the calculation, we find that the determinant is 2.

Step 6 ：Final Answer: The determinant of the given matrix is $2$