Find the Determinant [[-3/17,5/17],[4/17,-1/17]]

Problem

det(−3/17)

Solution

1. Identify the formula for the determinant of a 2×2 matrix [[a,b],[c,d]] which is a*d−b*c

2. Substitute the values from the given matrix into the formula: a=−3/17 b=5/17 c=4/17 and d=−1/17

3. Calculate the product of the diagonal elements a*d

(−3/17)*(−1/17)=3/289

4. Calculate the product of the off-diagonal elements b*c

(5/17)*(4/17)=20/289

5. Subtract the product of the off-diagonal elements from the product of the diagonal elements:

3/289−20/289=−17/289

6. Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 17

−(17÷17)/(289÷17)=−1/17

Final Answer

det(−3/17)=−1/17

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