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Let A=[a0 0 0a0 0 0a] , then A^n is equa...

Let `A=[a0 0 0a0 0 0a]` , then `A^n` is equal to `[a^n0 0 0a^n0 0 0a]` (b) `[a^n0 0 0a0 0 0a]` (c) `[a^n0 0 0a^n0 0 0a^n]` (d) `[n a0 0 0n a0 0 0n a]`

A

`[(na, 0,0),(0,nb,0),(0,0,nc)]`

B

`[(a,0,0),(0,b,0),(0,0,c)]`

C

`[(a^n , 0,0),(0,b^n , 0),(0,0,c^n)]`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. Let A=[a0 0 0a0 0 0a] , then A^n is equal to [a^n0 0 0a^n0 0 0a] (b) [...

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  2. If A and B are square martrices of equal degree, then which one is co...

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  3. If A=[(1,0,0),(0,1,1),(0,-2,4)],6A^-1=A^2+cA+dI, then (c,d)=

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  4. about to only mathematics

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  5. If A=[[alpha,0],[ 1, 1]] and B=[[1, 0],[ 5, 1]], find the values of al...

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  6. Let P=[a(i j)] be a 3xx3 matrix and let Q=[b(i j)],w h e r eb(i j)=2^(...

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  7. If A=|[alpha,2], [2,alpha]| and |A|^3=125 , then the value of alpha ...

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  8. The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,...

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  9. Let "f(x)"=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x...

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  10. The parameter on which the value of the determinant |[1,a...

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  11. The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

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  12. Consider the set A of all matrices of order 3 xx 3 with entries 0 or 1...

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  13. If A is a 3xx3 non-singular matrix such that A A' = A' A and B = A^(...

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  14. If P is a 3xx3 matrix such that P^(T) = 2 P + I , where P^(T) is the...

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  15. Let omega!=1 be cube root of unity and S be the set of all non-singula...

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  16. Let M and N be two 3xx3 nonsingular skew-symmetric matrices such that ...

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  17. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

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  18. Given , 2x-y+2z=2, x-2y+z=-4, x+y+lambdaz=4, then the value of lam...

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  19. The number of values of k for which the system of the equations (k+1)x...

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  20. If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero ...

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  21. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

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