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for a real number alpha if the system ...

for a real number `alpha` if the system
`[{:(1,,alpha,,alpha^(2)),(alpha,,1,,alpha),(alpha^(2),,alpha,,1):}][{:(x),(y),(z):}]=[{:(1),(-1),(1):}]` of linear equations has infinitely many solutions then `1+alpha+alpha^(2) = "______"`

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RESONANCE ENGLISH-MATRICES & DETERMINANT-EXERCISE-3
  1. Let a, b, and c be three real numbers satifying [(a, b, c)] [(1,9,7)...

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

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

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  6. If the adjoint of a 3xx3 matrix P is [[1,4,4],[2,1,7],[1,1,3]], then t...

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

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

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

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

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

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

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

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

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

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

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  20. Let P be a matrix of order 3 x 3 such that all the entries in P are f...

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