3A=(12221−2x2y) and A.AT =I then x + y

AAT=14(12221−2x2y)(12x2122−2y)=19(90x+4+2y092x+2−2yx+4+2y2x+2−2yx2+4+y2)=(100010001)⇒x+y=−3

3A=(12221−2x2y) and A.AT =I then x + y

AAT=14(12221−2x2y)(12x2122−2y)=19(90x+4+2y092x+2−2yx+4+2y2x+2−2yx2+4+y2)=(100010001)⇒x+y=−3

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$3 A = (\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ x & 2 & y \end{matrix}) a n d A . A^{T} = I$ then x + y

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Detailed Solution

$A A^{T} = \frac{1}{4} (\begin{matrix} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ x & 2 & y \end{matrix}) (\begin{matrix} 1 & 2 & x \\ 2 & 1 & 2 \\ 2 & - 2 & y \end{matrix}) = \frac{1}{9} (\begin{matrix} 9 & 0 & x + 4 + 2 y \\ 0 & 9 & 2 x + 2 - 2 y \\ x + 4 + 2 y & 2 x + 2 - 2 y & x^{2} + 4 + y^{2} \end{matrix})$