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If f(x)=[{:(cos x, -sin x, 0),(sin x, co...

If `f(x)=[{:(cos x, -sin x, 0),(sin x, cos x, 0),(0,0,1):}]`, then which of the following are correct ?
1. `f(theta) xx f(phi) = f(theta +phi)`.
2. The value of the determinant of the matrix `f(theta) xx f(phi)` is I.
3. The determinant of f(x) is an even number Select the correct answer using the codes given below :

A

A. Both 1 and 2

B

B. Both 2 and 3

C

C. Both 1 and 3

D

D. 1,2, and 3

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PUNEET DOGRA-MATRIX-PREV YEAR QUESTIONS
  1. What is [x y z ] [{:(a,h,g),(h,b,f),(g,f,c):}] equal to ?

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  2. If m=[{:(1,0),(0,1):}] and n=[{:(0,1),(-1,0):}], then what is the valu...

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  3. If f(x)=[{:(cos x, -sin x, 0),(sin x, cos x, 0),(0,0,1):}], then which...

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  4. The values of k for which the system of equations kx+y+z=0,x-ky+z=0 an...

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  5. If A=[{:(1,-1),(2,3):}] and B=[{:(2,3),(-1,-2):}] then which of the fo...

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  6. Consider the following for the next two itmes that follow : For the ...

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  7. Under what condition does the above system of equation have unique sol...

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  8. Consider the following in respect of the matrix A= [{:(-1,1),(1,-1):}]...

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  9. If A is a square matrix, then the value of adj A^(T)-(adj A)^(T) is eq...

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  10. If A=[{:(1,0,-2),(2,-3,4):}], then the matrix X for which 2x+3A=0 hold...

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  11. If A is an invertible matrix of order n and k is any positive real num...

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  12. The matrix A=[{:(1,3,2),(1,x-1,1),(2,7,x-3):}] will have inverse for e...

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  13. Match List 1 with List 2. Select the correct answer using the codes gi...

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  14. The matrix [{:(0,-4+i),(4+I,0):}] is

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  15. Which one of the following matrices is an elementary matrix ?

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  16. If A=[{:(2,7),(1,5):}] then what is A+3A^(-1) equal to ?

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  17. X=[{:(3,-4),(1,-1):}],B=[{:(5,2),(-2,1):}] and A=[{:(p,q),(r,s):}] the...

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  18. A[{:(x+y,y),(2x,x-y):}],B =[{:(2),(-1):}] and C [{:(3),(2):}]. If AB =...

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  19. v34

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  20. If A and B are two matrices of order 2 and det (A) is 3, det (B) is -1...

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