Maths-
General
Easy
Question
If k .
is an orthogonal matrix, then k is equal to-
- 1
- 1/2
- 1/3
- None of these
The correct answer is: 1/3
Let A = 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](data:image/png;base64,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)
Since A is orthogonal
AAT = I
k2
= I
9k2I = I
k2 = ![fraction numerator 1 over denominator 9 end fraction](data:image/png;base64,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)
k = ± ![fraction numerator 1 over denominator 3 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAKNJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLcATibUD8DYh/APEtIJ4AxMKkGrQfiIOAmA1JzACId1DLpZ+oYYgSEN+gxABxIE6EhpMXNbJMAaVeEgTiACA+CcT21AgjHqhhVAE/qGGIHjTASQIHgTgUiFmAmAma0u8DcTypBtkC8RaoV35AU7oPPg0ArQs4erRAu/EAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MzwvbW4+PC9tZnJhYz48L21hdGg+q+QgMwAAAABJRU5ErkJggg==)
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