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If {:E(theta)=[(cos^2 theta,costhetasint...

If `{:E(theta)=[(cos^2 theta,costhetasintheta),(costhetasintheta,sin^2theta)]:},and thetaand phi` differ by an odd multiple of `pi//2," then "E(theta)E(phi)` is a

A

Null matrix

B

Unit matrix

C

Diagonal matrix

D

None of these

Text Solution

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The correct Answer is:
C
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ML KHANNA-MATRICES-PROBLEM SET(1) (MULTIPLE CHOICE QUESTIONS)
  1. Let F(alpha)=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha, 0),(0,...

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  2. If E(theta)=[(cos theta, sin theta),(-sin theta, cos theta)], then E(a...

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  3. If {:E(theta)=[(cos^2 theta,costhetasintheta),(costhetasintheta,sin^2t...

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  4. If A=[(cos^(2) theta, cos theta sin theta),(cos theta sin theta, sin^(...

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  5. If A and B are matrices given below: A=[(0,c,-b),(-c,0,a),(b,-a,0)] ...

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  6. Let F(alpha)=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha, 0),(0,...

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  7. If F(alpha)=[(cos alpha, -sin alpha, 0),(sin alpha, cos alpha, 0),(0,0...

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  8. If [(1,-tan theta),(tan theta,1)][(1,tan theta),(-tan theta,1)]^(-1)=[...

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  9. Which of the following the following is correct?

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  10. If A be a skew symmetric matrix of odd order, then |A| is equal to

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  11. If A be a skew symmetric matrix of even order then |A| is equal to

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  12. If A=[(1,0),(1//2,1)] then A^(50) is

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  13. If A=[(a,0,0),(0,a,0),(0,0,a)] then A^(n)=

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  14. If P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]], A=[[1,1],[0,1]] and Q=PAP^T, ...

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  15. If A=[(1,2,-1),(-1,1,2),(2,-1,1)] then det [adj(adjA)]=

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  16. The equations x+2y+3z=1, 2x+y+3z=2,5x+5y+9z=4 have

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  17. The equations 2x-3y+6z=4, 5x+7y-14z=1 3x+2y-4z=0, have

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  18. x+y+z=6 x-y+z=2 2x+y-z=1 then x,y,z are respectively

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  19. The value of a fro which the system of equations ax+by+z=0,x+ay+z=0,x+...

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  20. There are two column vectors X=((x),(1)) and ((1,4),(5,2)) X is parall...

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