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If A=[(2,-1),( 3,-2)] , then A^n= [(1, ...

If `A=[(2,-1),( 3,-2)]` , then `A^n=` `[(1, 0),( 0,1)]` , if (a) `n` is an even natural number (b) `[(1 ,0),( 0, 1)]` , if `n` is an odd natural number (c) `[(1 ,0),( 0, 1)]` , if `n in N` (d) none of these

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The mean of first n odd natural number is (a) (n+1)/2 (b) n/2 (c) n (d) n^2

The smallest natural number is (a) 0 (b) 1 (c) -1 (d) None of these

If n is an odd natural number, then sum_(r=0)^n (-1)^r/(nC_r) is equal to

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If A=[(1,2),(0,1)], then A^n= (A) [(1,2n),(0,1)] (B) [(2,n),(0,1)] (C) [(1,2n),(0,-1)] (D) [(1,n),(0,1)]

If n is an even natural number , then sum_(r=0)^(n) (( -1)^(r))/(""^(n)C_(r)) equals

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If A=[(i,0), (0,i)],\ n in N , then A^(4n) equals [(0,i), (i,0)] (b) [(0 ,0) ,(0, 0)] (c) [(1, 0) ,(0, 1)] (d) [(0,i) ,(i,0)]

RD SHARMA ENGLISH-ADJOINTS AND INVERSE OF MATRIX-All Questions
  1. If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists ...

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  2. If for the matrix A ,\ A^3=I , then A^(-1)=(a)A^2 (b) A^3 (c) A (d) no...

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  3. If Aa n dB are two square matrices such that B=-A^(-1)B A ,t h e n(A+B...

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  4. If A=[(2 ,0 ,0),( 0 ,2 ,0),( 0 ,0 ,2)] , then A^5= (a) 5A (b) 10 A (c...

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  5. For non-singular square matrix A ,\ B\ a n d\ C of the same order th...

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  6. The matrix [(5 ,1 ,0), (3 ,-2 ,-4 ), (6 ,-1 ,-2b)] is a singular matri...

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  7. If d is the determinant of a square matrix A of order n , then the ...

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  8. If A is a matrix of order 3 and |A|=8 , then |a d j\ A|= (a) 1 (b)...

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  9. If A^2-A +I = 0, then the inverse of A is: (A) A+I (B) A (C) ...

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  10. If A and B are invertible matrices, which of the following statemen...

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  11. If A is a square matrix such that A^2 = I, then A^(-1) is equal to (i...

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  12. Let A=[(1, 2), (3,-5)] and B=[(1, 0), (0, 2)] and X be a matrix such t...

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  13. If A=[ (2 , 3) ,( 5 ,-2 )] , then find |A|

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  14. If A=1/3[(1,2,2),(2,1,-2),(x,2,y)] satisfies A^T A=I , then x+y= (a) ...

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  15. If A=[(1,0,1), (0,0,1),(a,b,2)] , then a I+b A+2A^2 equals (a) A (b) -...

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  16. If [(1,-tantheta),(tantheta,1)][(1,tantheta),(-tantheta,1)]^(-1)=[(a,-...

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  17. If a matrix A is such that 3A^3 +2A^2+5A+I= 0, then A^(-1) is equal to

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  18. If A is an invertible matrix of order 2, then det (A^(-1))is equal to...

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  19. If A=[(2,-1),( 3,-2)] , then A^n= [(1, 0),( 0,1)] , if (a) n is an ev...

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  20. If x ,\ y ,\ z are non-zero real numbers, then the inverse of the ma...

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