Home
Class 12
MATHS
Let A(alpha)=[(cosalpha, -sinalpha,0),(s...

Let `A_(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)]`, then :

A

`A_(alpha+beta)=A_(alpha)A_(beta)`

B

`A_(alpha)^(-1)=A_(-alpha)`

C

`A_(alpha)^(-1)=-A_(alpha)`

D

`A_(alpha)^(2)=-I`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-4 : Subjective Type Problems|5 Videos

  • MATRICES

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-4 : Subjective Type Problems|5 Videos

  • LOGARITHMS

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|19 Videos

  • PARABOLA

    VIKAS GUPTA (BLACK BOOK)|Exercise Exercise-5 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

If A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] , then

Let F(alpha)=[{:(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),(0,0,1):}] and G(beta)=[{:(cosbeta,0,sinbeta),(0,1,0),(-sinbeta,0,cosbeta):}] . Show that [F(alpha).G(beta)]^(-1)=G(-beta).F(-alpha) .

If F(alpha)=[(cosalpha, -sinalpha,0),(sinalpha, cosalpha, 0),(0,0,1)] and G(beta)=[(cosbeta, 0, sinbeta),(0, 1, 0),(-sinbeta, 0, cosbeta)], then [F(alpha)G(beta)]^-1 is equal to (A) F(-alpha)G(-beta) (B) G(-beta)F(-alpha0 (C) F(alpha^-1)G(beta^-1) (D) G(beta^-1)F(alpha^-1)

If F(alpha)=[[cosalpha, -sinalpha, 0], [sinalpha, cosalpha, 0], [0, 0, 1]] , where alphainR , then (F(alpha))^(-1)=

Statement 1: If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n [F(alpha)]^(-1)=F(-alpha)dot Statement 2: For matrix G(beta)=[[cosbeta,0,sinbeta],[0, 1, 0],[-sinbeta,0,cosbeta]]dot we have [G(beta)]^(-1)=G(-beta)dot

If A_(alpha)=[(cosalpha,sinalpha),(-sinalpha,cosalpha)] then (A_(alpha))^2=?

If A=[[cosalpha, -sinalpha, 0], [sinalpha, cosalpha, 0], [0, 0, 1]] , then (adjA)^(-1)=

Inverse of the matrix {:[(cosalpha,-sinalpha,0),(sinalpha,cosalpha ,0),(0,0,1)]:} is