For a real number , if the system bmatrix 1 & & ^2 & 1 & ^2 & & 1 bmatrix bmatrix x y z bmatrix = bmatrix 1 -1 1 bmatrix of linear equations, has infinitely many solutions, then 1+ + ^2=

JEE Advanced 2017 Mathematics question

For a real number , if the system

of linear equations, has infinitely many solutions, then

Answer: 1

Infinitely many solutions require the determinant to vanish: . For every equation reads

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Question ID VK-026637