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How many 3xx3 matrices M with entries fr...

How many `3xx3` matrices M with entries from `{0, 1, 2}` are there, for which the sum of the diagonal entries of `M^(T)M` is 5 ?

A

126

B

198

C

162

D

135

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The correct Answer is:
B
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VMC MODULES ENGLISH-MATRICES AND DETERMINANTS -JEE ADVANCED ARCHIVE
  1. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

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  2. Let P=[(1,0,0),(3,1,0),(9,3,1)] and Q = [q(ij)] be two 3xx3 matrices s...

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  3. How many 3xx3 matrices M with entries from {0, 1, 2} are there, for wh...

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  4. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

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  5. Let M and N be two 3xx3 matrices such that MN=NM. Further, if M ne N^(...

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  6. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

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  7. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

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  8. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

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  9. If the adjoint of a 3 xx 3 matrix P is [{:(,1,4,4),(,2,1,7),(,1,1,3):}...

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  10. Let X \ a n d \ Y be two arbitrary, 3xx3 , non-zero, skew-symmetric ma...

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  11. Which of the following values of alpha satisfying the equation |(1+alp...

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  12. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

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  13. Let alpha, lambda , mu in R.Consider the system of linear equations ...

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  14. Which of the following is(are) NOT of the square of a 3xx3 matrix with...

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  15. Let S be the set of all column matrices [(b(1)),(b(2)),(b(3))] such th...

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  16. M=[{:(sin^(4)theta,-1-sin^(2)theta),(1+cos^(2)theta,cos^(4)theta):}]=a...

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  17. Let M=[{:(0,1,a),(1,2,3),(3,b,1):}]and adj M =[{:(-1,,1,,-1),(8,,-6,,2...

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  18. For positive numbers x, y and z, the numerical value of the determinan...

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  19. The value of the determinant |(1,a,a^2-bc),(1,b,b^2-ca),(1,c,c^2-ab)| ...

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  20. If x=-9 is a root of |(x,3,7),(2,x,2),(7,6,x)|=0 then other two roots ...

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