If \( \begin{vmatrix} a-b & p-q & x-y \\ b-c & q-r & y-z \\ c-a & r-p & z-x \end{vmatrix} = k \begin{vmatrix} a & b & c \\ p & q & r \\ x & y & z \end{vmatrix} \), then what is the value of \( k \) ?
- A. -1
- B. 0 ✓
- C. \frac{1}{2}
- D. 1
Correct Answer: B. 0
Explanation
Applying the row operation R_1 \to R_1 + R_2 + R_3 in the first determinant makes all elements of the first row zero. Thus, the determinant evaluates to zero, which means k = 0.
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