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`[ [ cosalpha , -sinalpha ] , [ sinalpha , cosalpha ] ]= [ [1 , 0 ] , [ 0 , 1 ]]`

Answer

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A = [ [ cosalpha , sinalpha ], [ sinalpha , cosalpha ] ] ,then find | A |

A = [ [ 1 , 0 , 0 ] , [ 0 , cosalpha , sinalpha ] , [ 0 , sinalpha , - cosalpha ] ] , find |A|

Knowledge Check

  • If A=[[cosalpha, sinalpha], [-sinalpha, cosalpha]] , then A^(10)=

    A
    `[[cos10alpha, -sin10alpha], [sin10alpha, cos10alpha]]`
    B
    `[[cos10alpha, sin10alpha], [-sin10alpha, cos10alpha]]`
    C
    `[[cos10alpha, sin10alpha], [-sin10alpha, -cos10alpha]]`
    D
    `[[cos10alpha, -sin10alpha], [-sin10alpha, -cos10alpha]]`

  • If A=[[cosalpha, sinalpha], [-sinalpha, cosalpha]] and A(adjA)=[[k, 0], [0, k]] , then k=

    A
    `sinalphacosalpha`
    B
    `cos2alpha`
    C
    `0`
    D
    `1`

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

    A
    `[[cosalpha, -sinalpha, 0], [sinalpha, cosalpha, 0], [0, 0, 1]]`
    B
    `[[-cosalpha, sinalpha, 0], [sinalpha, -cosalpha, 0], [0, 0, 1]]`
    C
    `[[-cosalpha, sinalpha, 0], [sinalpha, cosalpha, 0], [0, 0, 1]]`
    D
    `[[cosalpha, sinalpha, 0], [-sinalpha, cosalpha, 0], [0, 0, 1]]`

    • Similar Questions

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    Evaluate the following: |[cosalpha, sinalpha],[sinalpha, cosalpha]|

    costheta-sintheta=cosalpha-sinalpha

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

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

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