GATE 2026 MN – Question 38
Let $x=(1,2,1)^T$, $b=(-16,-3,7)^T$, and $$P^{-1}=\begin{pmatrix}e&-6&-7\\f&9&11\\-1&-2&g\end{pmatrix}.$$ Given Px=b and Py=d with $d=(-16,0,7)^T$, find y₂.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (A) 29
Explanation
Because x=P⁻¹b and y=P⁻¹d, their difference is y−x=P⁻¹(d−b). Here d−b=(0,3,0)ᵀ, so multiply the second column by3. The second component changes by27. Therefore y₂=2+27=29, A; the unknown entries are unnecessary.