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If    A = \begin{bmatrix} \sin \theta +\cos \theta &0 \\ b+c & 5-c \end{bmatrix}  is a null matrix , then which of the following is FALSE ? 

  • Option 1)

    \theta =3\pi/4

  • Option 2)

    b = -5

  • Option 3)

    c = 5

  • Option 4)

    \theta =\pi/4

 

Answers (1)

best_answer

As we have learned

Null Matrix -

All the element of a matrix are Zero

- wherein

A= \left [ a_{ij} \right ] ,

a_{ij}= 0

 

 \begin{bmatrix} \sin \theta & 0 \\ b+c& 5-c \end{bmatrix} = \begin{bmatrix} 0 & 0\\ 0&0 \end{bmatrix}

\sin \theta + \cos \theta = 0 ; b+c = 0 ; 5 -c = 0

c= 5 \: \: and \: \: b= -5 ; Also\: \: \sin \theta = - \cos \theta

Thus \: \: \tan \theta = -1

Thus \theta = n \pi - \pi/4 

or   \theta = -\pi/4, 3\pi/4, 7\pi/4......

 

 

 

 

 


Option 1)

\theta =3\pi/4

Option 2)

b = -5

Option 3)

c = 5

Option 4)

\theta =\pi/4

Posted by

Himanshu

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