Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If the matrix $open square brackets table row 0 cell 2 beta end cell gamma row alpha beta cell negative gamma end cell row alpha cell negative beta end cell gamma end table close square brackets$ is orthogonal, then

$α$ = ± $\frac{1}{\sqrt{2}}$
$β$ = ± $\frac{1}{\sqrt{6}}$
$γ$ = ± $\frac{1}{\sqrt{3}}$
All of these

The correct answer is: All of these

since A is orthogonal,
AA´ = I
$open square brackets table row cell 4 beta to the power of 2 end exponent plus gamma to the power of 2 end exponent end cell cell 2 beta to the power of 2 end exponent minus gamma to the power of 2 end exponent end cell cell negative 2 beta to the power of 2 end exponent plus gamma to the power of 2 end exponent end cell row cell 2 beta to the power of 2 end exponent minus gamma to the power of 2 end exponent end cell cell alpha to the power of 2 end exponent plus beta to the power of 2 end exponent plus gamma to the power of 2 end exponent end cell cell alpha to the power of 2 end exponent minus beta to the power of 2 end exponent minus gamma to the power of 2 end exponent end cell row cell negative 2 beta to the power of 2 end exponent plus gamma to the power of 2 end exponent end cell cell alpha to the power of 2 end exponent minus beta to the power of 2 end exponent minus gamma to the power of 2 end exponent end cell cell alpha to the power of 2 end exponent plus beta to the power of 2 end exponent plus gamma to the power of 2 end exponent end cell end table close square brackets$ = $open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets$
$therefore$ $alpha$ = ± $fraction numerator 1 over denominator square root of 2 end fraction$ , $beta$ = ± $fraction numerator 1 over denominator square root of 6 end fraction$ , $gamma$ = ± $fraction numerator 1 over denominator square root of 3 end fraction$

Related Questions to study

If $A equals open square brackets table row cell cos to the power of 2 end exponent invisible function application theta end cell cell cos invisible function application theta sin invisible function application theta end cell row cell cos invisible function application theta sin invisible function application theta end cell cell sin to the power of 2 end exponent invisible function application theta end cell end table close square brackets$ and $B equals open square brackets table row cell cos to the power of 2 end exponent invisible function application phi end cell cell cos invisible function application phi sin invisible function application phi end cell row cell cos invisible function application phi sin invisible function application phi end cell cell sin to the power of 2 end exponent invisible function application phi end cell end table close square brackets$ are two matrices such that the product AB is the null matrix then $theta minus ϕ$ is equal to

If $A equals open square brackets table row cell cos to the power of 2 end exponent invisible function application theta end cell cell cos invisible function application theta sin invisible function application theta end cell row cell cos invisible function application theta sin invisible function application theta end cell cell sin to the power of 2 end exponent invisible function application theta end cell end table close square brackets$ and $B equals open square brackets table row cell cos to the power of 2 end exponent invisible function application phi end cell cell cos invisible function application phi sin invisible function application phi end cell row cell cos invisible function application phi sin invisible function application phi end cell cell sin to the power of 2 end exponent invisible function application phi end cell end table close square brackets$ are two matrices such that the product AB is the null matrix then $theta minus ϕ$ is equal to

If the lines of regression are 3x+12y=19 and 3y+9x=46 then $r subscript x y end subscript$ will be

If the lines of regression are 3x+12y=19 and 3y+9x=46 then $r subscript x y end subscript$ will be

If regression coefficient of y on x is $fraction numerator 8 over denominator 5 end fraction$ and that of x on y is $fraction numerator 2 over denominator 5 end fraction$ and the acute angle between the two lines is $alpha$ , then the value of $tan invisible function application alpha$ is

If regression coefficient of y on x is $fraction numerator 8 over denominator 5 end fraction$ and that of x on y is $fraction numerator 2 over denominator 5 end fraction$ and the acute angle between the two lines is $alpha$ , then the value of $tan invisible function application alpha$ is

parallel

The coefficient of correlation for the following data will be

The coefficient of correlation for the following data will be

For the following data

the value of r will be

For the following data

the value of r will be

The coefficient of correlation for the following will be approximately

The coefficient of correlation for the following will be approximately

parallel

If correlation between x and y is r, then between y and x correlation will be

If correlation between x and y is r, then between y and x correlation will be

If r=-0.97, then

If r=-0.97, then

If r=0.2, then linear correlation will be necessarily

If r=0.2, then linear correlation will be necessarily

parallel

Coefficient of correlation between x and y for the following data will be approximately

Coefficient of correlation between x and y for the following data will be approximately

Coefficient of correlation from the following data will be

Coefficient of correlation from the following data will be

Coefficient of correlation between x and y for the following data will be

Coefficient of correlation between x and y for the following data will be

parallel

Karl Pearson's correlation coefficient between x and y for the following data will be approximately

Karl Pearson's correlation coefficient between x and y for the following data will be approximately

Karl Pearson's coefficient of correlation between the marks in English and Mathematics by ten students will be

Karl Pearson's coefficient of correlation between the marks in English and Mathematics by ten students will be

The coefficients of correlation between the heights (in inches) of fathers and sons from the following data will be

The coefficients of correlation between the heights (in inches) of fathers and sons from the following data will be

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.