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If m=[{:(1,0),(0,1):}] and n=[{:(0,1),(-...

If `m=[{:(1,0),(0,1):}] and n=[{:(0,1),(-1,0):}]`, then what is the value of the determinant of `m cos theta - n sin theta` ?

A

A) -1

B

B) 0

C

C) 1

D

D) 2

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Knowledge Check

  • If I= [{:(,1,0),(,0,1):}], J=[{:(,0,1),(,-1,0):}]and B=[{:(,cos theta,sin theta),(,-sin theta,cos theta)]:}"then B"=

    A
    `Icos theta+J sin theta`
    B
    `Icostheta-Jsintheta`
    C
    `I sin theta+Jcos theta`
    D
    `-Icos theta+Jsin theta`
  • If 5 cos theta - 12 sin theta = 0 , then what is the value of ( 1+ sin theta + cos theta )/( 1 - sin theta + cos theta) ?

    A
    `5//4`
    B
    `5//2`
    C
    `3//2`
    D
    `3//4`
  • If I = ((1,0),(0,1)), J = ((0,1),(-1,0)) and B = ((cos theta , sin theta),(-sin theta, cos theta)) then B equals

    A
    `(cos theta ) I +(sin theta) J`
    B
    `(sin theta ) I + (cos theta) J`
    C
    `(cos theta) I - (sin theta)J`
    D
    `-(cos theta ) I + (sin theta) J`
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