Find the Determinant

Problem

det(−0.5084)

Solution

1. Apply the expansion formula for a 3×3 determinant along the first row.

D=(a_11)*((a_22)*(a_33)−(a_23)*(a_32))−(a_12)*((a_21)*(a_33)−(a_23)*(a_31))+(a_13)*((a_21)*(a_32)−(a_22)*(a_31))

2. Calculate the first term by multiplying the first element of the first row by its minor.

−0.5084*((−0.7936)*(−0.8571)−(3.4285)*(−0.5873))

−0.5084*(0.68019456−(−2.01355805))

−0.5084*(2.69375261)=−1.369503826924

3. Calculate the second term by multiplying the second element of the first row by its minor and applying the negative sign.

−(−0.1587)*((−0.8474)*(−0.8571)−(3.4285)*(0.1525))

0.1587*(0.72630654−0.52284625)

0.1587*(0.20346029)=0.032289148023

4. Calculate the third term by multiplying the third element of the first row by its minor.

0.6857*((−0.8474)*(−0.5873)−(−0.7936)*(0.1525))

0.6857*(0.49767802−(−0.121024))

0.6857*(0.61870202)=0.424244075114

5. Sum the results of the three terms to find the final determinant value.

−1.369503826924+0.032289148023+0.424244075114=−0.912970603787

Final Answer

det(−0.5084)=−0.912970603787

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