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Let `M` be a `3xx3` matrix satisfying `M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1 1]=[0 0 12]` Then the sum of the diagonal entries of `M` is _________.

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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. Let K be a positive real number and A=[(2k-1,2sqrt(k),2sqrt(k)),(2sqrt...

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  2. A system of equations lambdax +y +z =1,x+lambday+z=lambda, x + y + lam...

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  3. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

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  4. Let z=(-1+sqrt(3)i)/(2), where i=sqrt(-1), and r, s in {1, 2, 3}. Let ...

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  5. The total number of distinct x in R for which |{:(x,,x^(2),,...

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  6. For a real number, alpha if the system [{:(,1,alpha,alpha^(2)),(,alp...

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  7. Let P be a matrix of order 3xx3 such that all the entries in P a...

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  8. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

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  9. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

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  10. Let omega be the solution of x^(3)-1=0 with "Im"(omega) gt 0. If a=2 w...

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  11. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  12. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  13. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

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  14. If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an iden...

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  15. Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positiv...

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  16. Let a,b,c be real numbers with a^(2) +b^(2) +c^(2)=1. Then show tha...

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  17. The value of the determinant |(sintheta, costheta, sin2theta) , (sin(t...

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  18. Suppose f(x) is a function satisfying the following conditions: f(0)=...

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  19. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

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  20. Let a >0,d >-0. Find the value of the determinant |1/a1/(a(a+d))1/((a+...

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