Answer to Question #98545 in Algebra for Shaheli Chattopadhyay

Question

1. Decide which of the following are true or false. 10
If true, furnish the proof, and if false, give a
counter example.
(a) A U (B fl C) = (A U B) n C for any subset
A, B, C of a set U.
(b) 1 .2 1I z2 , = Iz 1 Z21 for any two complex
numbers z1 and z2, where Izi denotes the
absolute value (or modulus) of z.
(c) A linear equation with coefficients in
C\ R in one unknown can have a root which
is real.
(d) The system of equations
4x + 6y = 9
6x + 9y = 1 3
is inconsistent.
(e) For a 3 x 3 matrix A
det (a A) = a (det A)
holds for every scalar a where det A denotes
the determinant of A.
2. (a) Prove that (ax + by) (ay + bx) 4abxy where 2
a, b, x, y are positive real numbers.
(b) Find all the four complex fourth roots of 3
( — 1). Show that these roots are in G.P.

Answer 1

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