# II-B.Tech. I-Semester Supplementary Examinations, May/June-2004

Jun 21st, 2015
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Find the values of a and b for which the equations x + ay + z = 3, x + 2y + 2z = b, x + 5y + 3z = 9 are consistent. When will these equations have a unique solution?

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Code No: NR/RR-210101II-B.Tech. I-Semester Supplementary Examinations, May/June-2004MATHEMATICS - II(Common to all Branches except Bio-Technology)Time: 3 HoursMax. Marks: 80Answer any FIVE questionsAll questions carry equal marks- - -1.a) Find the values of a and b for which the equationsx + ay + z = 3, x + 2y + 2z = b, x + 5y + 3z = 9are consistent. When will these equations have a unique solution? b) Investigate for what values of , the simultaneous equations.x + y + z = 6, x + 2y + 3z = 10, x + 2y + z = have (i) no solution (ii) a unique solution (iii) an infinite number of solutions.2.a)If is an eigen value of A then prove that the eigen value of B = a0A2 + a1A + a2I is a0 2 + a1 + a2. b)Find the eigen values and eigen vectors of 3.a)Show that any square matrix A = B + C where B is symmetric and C is skew-symmetric matrices. b)Determine a, b, c so that A is orthogonal where .4.Expand as a Fourier series.5.a)Find the half range sine series for the function f(x) = t-t2, 0

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