Find the Determinant [[7,9],[-2,-5]]

Problem

det(7)

Solution

1. Identify the elements of the 2×2 matrix [[a,b],[c,d]] where a=7 b=9 c=−2 and d=−5

2. Apply the formula for the determinant of a 2×2 matrix, which is det(A)=a*d−b*c

3. Substitute the values into the formula to calculate the product of the main diagonal and the product of the off-diagonal.

det(7)=(7)*(−5)−(9)*(−2)

4. Simplify the expression by performing the multiplication and subtraction.

(7)*(−5)=−35

(9)*(−2)=−18

−35−(−18)=−35+18

−35+18=−17

Final Answer

det(7)=−17

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