NCERT Class 12 Maths · Chapter 4 Determinants · Miscellaneous Exercise Question 7

✅ Step-by-Step Solution

1. The original equations require x,y,z≠0. Set u=1/x, v=1/y, w=1/z.
2. The transformed system has coefficient matrix \(\left[\begin{matrix}2 & 3 & 10\\4 & -6 & 5\\6 & 9 & -20\end{matrix}\right]\) and right-hand vector \(\left[\begin{matrix}4\\1\\2\end{matrix}\right]\). Its determinant is \(1200\), nonzero.
3. The inverse is \(\left[\begin{matrix}\frac{1}{16} & \frac{1}{8} & \frac{1}{16}\\\frac{11}{120} & - \frac{1}{12} & \frac{1}{40}\\\frac{3}{50} & 0 & - \frac{1}{50}\end{matrix}\right]\), so (u,v,w)ᵀ=A⁻¹B=\(\left[\begin{matrix}\frac{1}{2}\\\frac{1}{3}\\\frac{1}{5}\end{matrix}\right]\).
4. Each component is nonzero; taking reciprocals gives (x,y,z)ᵀ=\(\left[\begin{matrix}2\\3\\5\end{matrix}\right]\). Substitute the reciprocals into the original equations to check.