engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Linear Algebra Systems of Linear Equations
The system of linear equations in real (x, y) given by
\(\rm \begin{pmatrix} \rm x & \rm y \end{pmatrix} \begin{bmatrix} 2 & 5- 2 α \\\ α & 1 \end{bmatrix} = \rm \begin{pmatrix} \rm 0 & \rm 0 \end{pmatrix} \)
involves a real parameter α and has infinitely many non-trivial solutions for special value(s) of α. Which one or more among the following options is/are non-trivial solution(s) of (x, y) for such special value(s) of α ?
1
x = 2, y = −2
2
x = −1, y = 4
3
x = 1, y = 1
4
x = 4, y = −2