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January 19, 2022 8:35 pm 30 pts
uA- bis a ma a matrIX With eigen values y6 and-6, then the values of a and D are respectively, (Question ID = 2116] 1. 2 and-1. [Opton ID = 8463] 2. 2 and-2. [opton ID = 8464] 3. 2 and 1. [0ption ID = 8461] 4.-2 and 1. [Option 1D = 8462] Correct Answer:- 2 and-2. [Option ID = 8464] 41) 1he dimension of the vector space of all6 x6 real skew-symmetric matrices 1s [Question ID = 2126] 1. 36 [Option 1D = 8504] 2. 21 [Option ID = 8502] 3. 30 [Option ID = 8503] 4. 15 [Option ID = 8501] Correct Answer- 15 [Option ID = 8501] - ***** ****************** 42) Let (Xof (xo)) = (0, -1), (X,.f(x)) = (1, a) and (x2.f (x2)) = (2, b). If the first order divided differences f[X0, X1] = 5 and f[X1, X2]=c and the second order divided difference f[X0, X1, X2] then the values of a, b and c are [Question ID = 2148] 4, 2, 4 rOption 1D = 8592] 2, 4, 6. (option ID = 8590] 2. 34, 6, 2. [Option ID = 8589] 3 6, 2, 4 [Option ID = 8591] Correct Answer 4, 6, 2 [option 1D = 8589] 43) Let the polynomial f(x) = 3x+ 15x-20x+ 10x+ 20 e Zx], and fo(x) be the polynomial in Zz[x] obtained by reducing the coefficients of fx) modulo 3. Which one of the following statements is true? [Question ID = 2124] f(x) is reducible over Q, fox) is reducible over Z. [Option ID = 8496) fx) is irreducible over Q. f6x) is reducible over2 [Option ID = 8495] fx) is reducible over Q, fox) is ireducible over Zg. 3. [Option ID = 8494] f) is irreducible over Q, fo(x) is irreducible over Zg. [Option ID = 8493)
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• Navdeep goyal 1
40 tr(A)=0 and det(A)=-6 so a+b=0 ab-2=-6 => ab=-4 a=2,b=-2 41 6(6-1)/2= 15 42 a+1/1-0=5 a=4 b-a/2-1=c =>b-4=c so b=6 c=2 