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Maths-

General

Easy

Question

If k $open square brackets table row cell negative 1 end cell 2 2 row 2 cell negative 1 end cell 2 row 2 2 cell negative 1 end cell end table close square brackets$ is an orthogonal matrix then k is equal to

1
1/3
½
none of these

The correct answer is: 1/3

since A is orthogonal $therefore$ AA^T = I
$rightwards double arrow$ k^{2 $open square brackets table attributes columnalign center center center columnspacing 1em end attributes row cell negative 1 end cell 2 2 row 2 cell negative 1 end cell 2 row 2 2 cell negative 1 end cell end table close square brackets$} $open square brackets table row cell negative 1 end cell 2 2 row 2 cell negative 1 end cell 2 row 2 2 cell negative 1 end cell end table close square brackets$ = I
$rightwards double arrow$ k² $open square brackets table row 9 0 0 row 0 9 0 row 0 0 9 end table close square brackets$ = I
$rightwards double arrow$ 9k²I = I $rightwards double arrow$ k = ± 1/3

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