If 3A=12221−2x2y and AA′=I, then 3A=12221−2x2y and AA′=I, then x+y is equal to

(3A)′=12x2122−2yNow, 9I=(3A)(3A)′=12221−2x2y12x2122−2y=90x+4+2y092x+2−2yx+4+2y2x+2−2yx2+4+y2⇒x+2y+4=02x−2y+2=0x2+y2+4=9⇒x=−2, y=−1

If 3A=12221−2x2y and AA′=I, then 3A=12221−2x2y and AA′=I, then x+y is equal to

(3A)′=12x2122−2yNow, 9I=(3A)(3A)′=12221−2x2y12x2122−2y=90x+4+2y092x+2−2yx+4+2y2x+2−2yx2+4+y2⇒x+2y+4=02x−2y+2=0x2+y2+4=9⇒x=−2, y=−1

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If $3 A = [\begin{array}{ccc} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ x & 2 & y \end{array}]$ and $A A^{'} = I,$ then $3 A = [\begin{array}{ccc} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ x & 2 & y \end{array}] and A A^{'} = I, then x + y$ is equal to

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Detailed Solution

$(3 A)^{'} = [\begin{array}{ccc} 1 & 2 & x \\ 2 & 1 & 2 \\ 2 & - 2 & y \end{array}]$

Now, $9 I = (3 A) (3 A)^{'}$

$\begin{array}{l} = [\begin{array}{ccc} 1 & 2 & 2 \\ 2 & 1 & - 2 \\ x & 2 & y \end{array}] [\begin{array}{ccc} 1 & 2 & x \\ 2 & 1 & 2 \\ 2 & - 2 & y \end{array}] \\ = [\begin{array}{ccc} 9 & 0 & x + 4 + 2 y \\ 0 & 9 & 2 x + 2 - 2 y \\ x + 4 + 2 y & 2 x + 2 - 2 y & x^{2} + 4 + y^{2} \end{array}] \end{array}$