AP ICET 2019 Shift 2 Paper

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Question : 132 of 200

Marks: +1, -0

If A =

[\table 1,-1;2,-1]

, B =

[\table x,1;y,-1]

and

(A+B)^2

=

A^2+B^2

, then (x, y) =

(- 2 , - 2)
(1 , 4)
(- 1 , 4)
(1 , - 4)

Solution:

Since

(A + B)^2 = A^2 + B^2

⇒ AB + BA = 0

[\table x-y , 2 ; 2-y , 3]+[\table x+2 , -x-1 ; y-2 , -y+1]=0

[\table 2 x-y+2 , -x+1 ; 0 , -y+4]=[\table 0 , 0 ; 0 , 0]

∴ x = 1, y = 4

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