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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

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
C
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DISHA PUBLICATION-MATRICES-Exercise 1: Concept Builder (Topic 2)
  1. If A and B are 2xx2 matrices, then which of the following is true ?

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  2. If p, q, r are 3 real number satisfying the matrix equation, [p q r][[...

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  3. If f(x)=x^(2)+4x-5andA={:[(1,2),(4,-3)]:}, then f(A) is equal to

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  4. If [(1,x,1)][(1,3,2),(0,5,1),(0,3,2)][(x),(1),(-2)]=[0] then x is

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  5. 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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  6. Which is true about matirx multiplication?

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  7. If R(t)=[(cost,si nt),(-si nt,cost)], then R(s)R(t) equals

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  8. If [(alpha,beta),(gamma,-alpha)] is square root of identity matrix of ...

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  9. If A=[(1,0),(3,-1),(-5,2)] and B=[(1,-2),(-2,2),(1,1)] , then find the...

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  10. Find matrices X, if 2X-Y=[(6,-6,0),(-4,2,1)] and X+2Y=[(3,2,5),(-2,1,-...

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  11. If A=[(1,2,8)],B=[(4),(5),(6)], and C=[(0,2,0)] and D=[(5),(2),(4)], t...

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  12. If [(2,0,7),(0,1,0),(1,-2,1)][(-x,14x,7x),(0,1,0),(x,-4x,-2x)]=[(1,0,0...

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  13. If A is involuntary matrix and I is unit matrix of the same order then...

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  14. Suppose a matrix A satisfies A^(2)-5A+7I=0. If A^(8)=aA+bI, find a-b.

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  15. If {:A=[(0,1),(1,0)]:},I is the unit matrix of order 2 and a, b are a...

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  16. If A is a square matrix such that A^2=A ,t h e n(I+A)^3-7A is equal to...

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  17. Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and 11 - n ...

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

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  19. If {:A=[(costheta,sintheta),(-sintheta,costheta)]:}, " then "underset(...

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  20. If matrix A=([a(i j)])(2xx2) , where a(i j)={1,\ if\ i!=j0,\ if\ i+j ,...

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