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If A=[{:(a,b),(b,a):}] and A^(2)=[{:(alp...

If `A=[{:(a,b),(b,a):}] and A^(2)=[{:(alpha, beta),(beta, alpha):}]` then

A

`alpha=a^2+b^2,beta=ab`

B

`alpha=a^2+b^2,beta=2ab`

C

`alpha=a^2+b^2,beta=a^2-b^2`

D

`alpha=2ab,beta=a^2+b^2`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise
  1. If A=[(cosx,sinx),(-sinx,cosx)] and A.(adjA)=k[(1,0),(0,1)] then the v...

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  2. If A=[[1,1],[1,1]] ,prove that A^n=[[2^(n-1),2^(n-1)],[2^(n-1),2^(n-1)...

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  3. If A=[{:(a,b),(b,a):}] and A^(2)=[{:(alpha, beta),(beta, alpha):}] the...

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  4. If A is an invertible square matrix; then adj A^T = (adjA)^T

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  5. If A=[[1,3] , [3,4]] and A^2-kA-5I2=0 then k=

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  6. If A=[a(ij)] is a scalar matrix, then trace of A is

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  7. If A=[a(i j)] is a scalar matrix of order nxxn such that a(i i)=k f...

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  8. If A=[a(i j)] is a scalar matrix of order nxxn such that a(i i)=k f...

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  9. If A=[a(ij)] is a scalar matrix of order nxxn and k is a scalar, then ...

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  10. If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],...

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  11. If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0...

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  12. Find the matrix A satisfying the matrix equation [{:(2,1),(3,2):}]A[...

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

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  14. If A and B are two matrices such that A+B and AB are both defind, then

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  15. If a matrix A is such that 3\ A^3+2\ A^2+5\ A+I=0 , then A^(-1) is equ...

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  16. Let A and B be matrices of order 3 xx 3. If AB = 0, then which of the ...

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  17. If A is an invertible matrix, then which of the following is correct

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  18. Which of the following is/are incorrect? (i) adjoint of a symmetri...

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  19. If [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed ...

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  20. If for matrix A,A^(2)+l=0, where l is the identity matrix, then A equa...

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