NCERT Class 12 Maths · Chapter 3 Matrices · Miscellaneous Exercise Question 3

✅ Step-by-Step Solution

1. The three columns are pairwise orthogonal: each cross dot product cancels to zero.
2. Their squared norms are 2x²,6y²,3z², so AᵀA=\(\left[\begin{matrix}2 x^{2} & 0 & 0\\0 & 6 y^{2} & 0\\0 & 0 & 3 z^{2}\end{matrix}\right]\).
3. Equating to I gives x²=1/2,y²=1/6,z²=1/3. Either sign is allowed independently, yielding eight triples.