The system of linear equations in real (x, y) given by \left(\begin{array}{cc}x & y)\end{array}\left[\begin{array}{cc}2 & 5-2 \alpha \ \alpha & 1]\end{array}=\left(\begin{array}{cc}0 & 0)\end{array} 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 ?

GATE Mechanical Engineering (ME) 2022 Shift 1 Solved Paper

Question : 46 of 65

Marks: +1, -0

The system of linear equations in real (x, y) given by

{(\table x , y)}{[\table 2 , 5-2 α ; α , 1]}={(\table 0 , 0)}

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 ?

x = 2, y = −2
x = −1, y = 4
x = 1, y = 1
x = 4, y = −2

Validate

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