Find the Determinant of the Resulting Matrix

Problem

det(([−9,8],[1,1])*([−34,0],[0,34])*([−1/17,8/17],[1/17,9/17]))

Solution

1. Identify the property of determinants for the product of matrices. The determinant of a product of square matrices is the product of their individual determinants.

det(A*B*C)=det(A)*det(B)*det(C)

2. Calculate the determinant of the first matrix A

det(A)=(−9)*(1)−(8)*(1)

det(A)=−9−8=−17

3. Calculate the determinant of the second (diagonal) matrix B

det(B)=(−34)*(34)−(0)*(0)

det(B)=−(34⋅34)=−34(2*n)

4. Calculate the determinant of the third matrix C

det(C)=(−1/17)*(9/17)−(8/17)*(1/17)

det(C)=−9/289−8/289=−17/289

det(C)=−1/17

5. Multiply the individual determinants together to find the final result.

det(A*B*C)=(−17)⋅(−34(2*n))⋅(−1/17)

det(A*B*C)=−34(2*n)

Final Answer

det(([−9,8],[1,1])*([−34,0],[0,34])*([−1/17,8/17],[1/17,9/17]))=−34(2*n)

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