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Maths-

General

Easy

Question

If 3A = $open square brackets table row 1 2 2 row 2 1 cell negative 2 end cell row x 2 y end table close square brackets$ and A. A^t = I, then x + y equal to

–1
1
2
None of these

The correct answer is: None of these

AA^–1= $1 over 9$ $open square brackets table row 1 2 2 row 2 1 cell negative 2 end cell row x 2 y end table close square brackets$
$open square brackets table row 1 2 x row 2 1 2 row 2 cell negative 2 end cell y end table close square brackets$ = $1 over 9$ $open square brackets table row 9 0 cell x plus 4 plus 2 y end cell row 0 9 cell 2 x plus 2 minus 2 y end cell row cell x plus 4 plus 2 y end cell cell 2 x plus 2 minus 2 y end cell cell x to the power of 2 end exponent plus 4 plus y to the power of 2 end exponent end cell end table close square brackets$
I = $open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets$
$rightwards double arrow$ x = –2, y = –1
$rightwards double arrow$ x + y = – 3

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