Determinants
General
Grade 12
Question:
If $x > m, y > n, z > r$ ($x, y, z > 0$) such that $\begin{vmatrix} x & n & r \\ m & y & r \\ m & n & z \end{vmatrix} = 0$, then the value of $\frac{x}{x-m} - 1 + \frac{y}{y-n} - 1 + \frac{z}{z-r} - 1$ is
Step-by-Step Solution
Key Concept: General
From the result of Illustration 30, we know that: <br> $\frac{x}{x-m} + \frac{y}{y-n} + \frac{z}{z-r} = 2$ <br> The required expression is: <br> $\left(\frac{x}{x-m} - 1\right) + \left(\frac{y}{y-n} - 1\right) + \left(\frac{z}{z-r} - 1\right) = \left(\frac{x}{x-m} + \frac{y}{y-n} + \frac{z}{z-r}\right) - 3$ <br> $= 2 - 3 = -1$
Correct Answer: D