The values of `theta`, `lambda` for which the following equations `sinthetax-costhetay+(lambda+1)z=0` , `costhetax+sinthetay-lambdaz=0` , `lambdax+(la

Question

The values of `theta`, `lambda` for which the following equations `sinthetax-costhetay+(lambda+1)z=0` , `costhetax+sinthetay-lambdaz=0` , `lambdax+(la

The values of `theta`, `lambda` for which the following equations `sinthetax-costhetay+(lambda+1)z=0` , `costhetax+sinthetay-lambdaz=0` , `lambdax+(lambda+1)y+costhetaz=0`
have non trivial solution, is
A. `theta=npi`, `lambda in R-{0}`
B. `theta=2npi`, `lambda` is any rational number
C. `theta=(2n+1)pi`, `lambda in R^(+)`, `n in I`
D. `theta=(2n+1)(pi)/(2)`, `lambda in R`, `n in I`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

If `I_(1)=int_(0)^(1)(dx)/(e^(x)(1+x))` and `I_(2)=int_(0)^(pi//4)(e^(tan^(7)theta)sintheta)/((2-tan^(2)theta)cos^(3)theta d theta`,then find the valu

2 Answers 6 Views

Let `A=[{:(,sin theta,1sqrt2),(,-1//sqrt2,cos theta),(,cos theta,tan theta):}]& B=[{:(,1sqrt2,sin theta),(,cos theta,cos theta),(,cos theta,-1):}]`. F

2 Answers 4 Views

Prove the orthogonal matrices of order two are of the form `[(cos theta,-sin theta),(sin theta,cos theta)]` or `[(cos theta,sin theta),(sin theta,-cos

2 Answers 7 Views

If `theta-phi=pi/2,` prove that, `[(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,

2 Answers 5 Views

If `A(theta)=[(sin theta, i cos theta),(i cos theta, sin theta)]`, then which of the following is not true ?

2 Answers 7 Views

सरल कीजिए, ` cos theta [{:( cos theta,, sin theta ), (-sin theta,, cos theta ):}] + sin theta [ {:(sin theta ,, - cos theta ), (cos theta ,, sin theta

2 Answers 4 Views

If the equations `4x^(2)-x-1=0` and `3x^(2)+(lambda+mu)x+lambda-mu=0` have a root common, then the rational values of `lambda` and `mu` are

2 Answers 5 Views

Find all values of `lambda` for which the `(lambda-1)x+(3lambda+1)y+2lambdaz=0(lambda-1)x+(4lambda-2)y+(lambda+3)z=0 2x+(3lambda+1)y+3(lambda-1)z=0` p

2 Answers 5 Views

If `A=[{:(8,-6,2),(-6,7,-4),(2,-4,3):}]` and `X` is a non zero column matrix such that `AX=lambdaX`, where `lambda` is a scalar, then values of `lambd

2 Answers 4 Views

A spectroscopic instrument can resolve two nearly wavelength `lambda and lambda = Delta lambda if lambda//Delta lambda` is smaller than `8000` This is

2 Answers 5 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - D
`(d)` For an trivial solution `|{:(sintheta,-costheta,lambda+1),(costheta,sintheta,-lambda),(lambda,lambda+1,costheta):}|=0`
`impliessin^(2)thetacostheta+lambda^(2)costheta+(lambda+1)^(2)costheta-sinthetalambda(lambda+1)+cos^(3)theta+sinthetalambda(lambda+1)=0`
`implies(sin^(2)theta+cos^(2)theta)costheta+lambda^(2)costheta+(lambda+1)^(2)costheta=0`
`impliescostheta+lambda^(2)costheta+(lambda+1)^(2)costheta=0`
`implies2costheta(lambda^(2)+lambda+1)=0`
`impliescostheta=0`
`impliestheta=(2n+1)(pi)/(2)`, `lambda in R`, `n in I`