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

    VK JAISWAL ENGLISH|Exercise Exercise-3 : Matching Type Problems|4 Videos

  • MATRICES

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|5 Videos

  • MATRICES

    VK JAISWAL ENGLISH|Exercise Exercise-4 : Subjective Type Problems|5 Videos

  • LOGARITHMS

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|19 Videos

  • PARABOLA

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|2 Videos

Similar Questions

Explore conceptually related problems

If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],t h e n prove that [F(alpha)]^(-1)=F(-alpha)dot

If A=[(cosalpha,-sinalpha,0),(sinalpha,cosalpha,0),( 0, 0, 1)], find a d jdotA and verify that A(a d jdotA)=(a d jdotA)A=|A|I_3dot

If A(alpha,beta)=[[cosalpha,sinalpha,0],[-sinalpha,cosalpha,0],[ 0, 0,e^(beta)]],t h e nA(alpha,beta)^(-1) is equal to a. A(-alpha,-beta) b. A(-alpha,beta) c. A(alpha,-beta) d. A(alpha,beta)

Let F(alpha)=[cosalpha-sinalpha0sinalphacosalpha0 0 0 1] and G(beta)=[cosbeta0sinbeta0 1 0-sinbeta0cosbeta] . Show that [F(alpha)]^(-1)=F(-alpha) (ii) [G(beta)]^(-1)=G(-beta) (iii) [F(alpha)G(beta)]^(-1)=G(-beta)F(-alpha) .

If A=[{:(sinalpha,-cosalpha,0),(cosalpha,sinalpha,0),(0,0,1):}] then A^(-1) is equal to

If A=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]] , find a d j\ A and verify that A(a d j\ A)=(a d j\ A)A=|A|I_3 .

Let A=({:(cosalpha,-,sinalpha),(sinalpha,,cosalpha):}),(alphaepsilonR) such that A^(32)=({:(0,-1),(1,0):}) . Then a value of alpha is:

If A_alpha=[[cosalpha ,sinalpha],[-sinalpha,cosalpha]] , then prove that A_alphaA_beta=A_(alpha+beta) for every positive integer n .

If A=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] is identity matrix, then write the value of alpha .

Let A=[(cos alpha,sin alpha),(-sinalpha,cosalpha)] and matrix B is defined such that B=A+3A^(2)+3A^(3)+A^(4). If |B|=8 then the number of values of alpha in [0, 10pi] is