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Question

If $A equals open square brackets table attributes columnalign center center center center columnspacing 1em end attributes row cell cos squared end cell alpha cell cos invisible function application horizontal ellipsis horizontal ellipsis end cell cell alpha sin invisible function application horizontal ellipsis horizontal ellipsis end cell row cell cos invisible function application horizontal ellipsis end cell cell alpha sin end cell alpha cell sin squared invisible function application alpha end cell end table close square brackets$ and $A equals open square brackets table attributes columnalign center center center center columnspacing 1em end attributes row cell cos squared end cell beta cell cos invisible function application horizontal ellipsis sin end cell alpha row cos cell beta sin end cell cell sin squared invisible function application beta end cell beta end table close square brackets$ are two matrices such that the product AB is null matrix, then $alpha minus beta$ is

0
Multiple of $π$
An odd multiple of $π$ /2
None of the above

The correct answer is: An odd multiple of $pi$ /2

Given, AB = 0
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell therefore open square brackets table attributes columnalign center columnspacing 1em end attributes row cell cos squared invisible function application alpha cos invisible function application alpha sin invisible function application alpha end cell row cell cos invisible function application alpha sin invisible function application alpha sin squared invisible function application alpha end cell end table close square brackets cross times open square brackets table attributes columnalign center columnspacing 1em end attributes row cell cos squared invisible function application beta cos invisible function application beta sin invisible function application beta end cell row cell cos invisible function application beta sin invisible function application beta sin invisible function application beta end cell end table close square brackets end cell row cell equals open square brackets table attributes columnalign left left columnspacing 1em end attributes row 0 0 row 0 0 end table close square brackets end cell row cell not stretchy rightwards double arrow open square brackets table attributes columnspacing 1em end attributes row cell cos invisible function application alpha cos invisible function application beta cos invisible function application left parenthesis alpha minus beta right parenthesis cos invisible function application alpha sin invisible function application beta cos invisible function application left parenthesis alpha minus beta right parenthesis end cell row cell cos invisible function application beta sin invisible function application alpha cos invisible function application left parenthesis alpha minus beta right parenthesis sin invisible function application alpha sin invisible function application beta cos invisible function application left parenthesis alpha minus beta right parenthesis end cell end table close square brackets end cell row cell equals open square brackets table attributes columnalign left left columnspacing 1em end attributes row 0 0 row 0 0 end table close square brackets end cell row cell not stretchy rightwards double arrow cos invisible function application left parenthesis alpha minus beta right parenthesis equals 0 end cell row cell not stretchy rightwards double arrow alpha minus beta text is an odd multiple of end text pi over 2 end cell end table$

Related Questions to study

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parallel

Which of the following functions is one-to -one?

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parallel

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parallel

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If denotes the set of all real numbers, then the function $f colon R not stretchy rightwards arrow R$ defined by $f left parenthesis x right parenthesis equals vertical line x vertical line$ is

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parallel

If $f colon R not stretchy rightwards arrow C$ is defined by $f left parenthesis x right parenthesis equals e to the power of 2 i x end exponent$ for $x element of R$ , then $f$ is (where C denotes the set of all complex numbers)

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Let $f colon N not stretchy rightwards arrow N$ defined by $f left parenthesis x right parenthesis equals x squared plus x plus 1 comma x element of N$ , then $f$ is

parallel

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