Linear Algebra

Step 1: Understanding the determinant.
We are given the determinant of two 3x3 matrices. The equation can be solved by equating the determinants of both matrices. First, we calculate the 2x2 determinants: Substitute these into the determinant equation: Simplifying the expression: Step 2: Solve for the value of .
Now solve for by equating the determinant of the second matrix: The determinant of the right-hand matrix: Now calculating the 2x2 determinants: Substitute these back into the determinant expression: Thus, the determinant equals 0. Hence, the correct option for is .
Final Answer: