Find the Determinant [[3,-2,1],[1,-3,4],[1,-2,0]]

Problem

det(3)

Solution

1. Set up the expansion along the first row using the cofactor method.

2. Calculate the first term by multiplying the element 3 by the determinant of its 2×2 minor.

3⋅det(−3)=3*((−3)*(0)−(4)*(−2))

3*(0+8)=24

3. Calculate the second term, remembering to negate the sign for the element at position (1,2)

−(−2)⋅det(1)=2*((1)*(0)−(4)*(1))

2*(0−4)=−8

4. Calculate the third term by multiplying the element 1 by the determinant of its 2×2 minor.

1⋅det(1)=1*((1)*(−2)−(−3)*(1))

1*(−2+3)=1

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

24−8+1=17

Final Answer

det(3)=17

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