a. Find the value of B, if 78-3-7 4 1] -3 -1 21 b. If A-...

 

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a. Find the value of B, if 78-3-7 4 1] -3 -1 21 b. If A- 1 3.B-1 8 5 and C- [3]then find the -1 21 -5 1 31 following: 1. C +C 2. AT-2B c. Find the derivative of y=+cosx Question-2 (1.5+2.5 marks) a. Solve the following system of linear equations by Gauss Jordan method x+y=33x+2y= 7 A b. Find the eigen values and eigen vectors of the matrix 4 = [4] Question-3 (2.5+1.5 marks) a. Show that (Q\{0), ) is an abelian (commutative) group where is define a+b=ab b. Find all the cyclic subgroups of the group (Z+)- Question-4 (1.5+1+1.5 marks) a. If G={1,-1,-). In a group (G, x) [Hint: 2-1 ori-1] 1. Show that G is closed under x. 2. Show that (G, x) is a cyclic group generated by i. 1FL-Mathematics for IT Page a. Find the value of B, if 78-3-7 4 1] -3 -1 21 b. If A- 1 3.B-1 8 5 and C- [3]then find the -1 21 -5 1 31 following: 1. C +C 2. AT-2B c. Find the derivative of y=+cosx Question-2 (1.5+2.5 marks) a. Solve the following system of linear equations by Gauss Jordan method x+y=33x+2y= 7 A b. Find the eigen values and eigen vectors of the matrix 4 = [4] Question-3 (2.5+1.5 marks) a. Show that (Q\{0), ) is an abelian (commutative) group where is define a+b=ab b. Find all the cyclic subgroups of the group (Z+)- Question-4 (1.5+1+1.5 marks) a. If G={1,-1,-). In a group (G, x) [Hint: 2-1 ori-1] 1. Show that G is closed under x. 2. Show that (G, x) is a cyclic group generated by i. 1FL-Mathematics for IT Page