Let A = i - i - i i , i = - 1 . Then, the system of linear equations A 8 x y = 8 64 has :

Let A=i-i-ii,i=-1. Then, the system of linear equations A8xy=864 has :
  1. A unique solution
  2. Infinitely many solutions
  3. No solution
  4. Exactly two solutions

Solution

A=i-i-ii

A2=-222-2=2-111-1

A4=222-2-22=81-1-11

A8=642-2-22=1281-1-11

A8xy=864

⇒1281-1-11xy=864

⇒128x-y-x+y=864

⇒x-y=116   ...(1)

and -x+y=12   ...(2)

⇒ From (1) and (2) : No solution.

Asked in: JEE Main 2021 (16 Mar Shift 1)

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