There are four questions and they are attached below.

write neatly and clearly. Thank you

Linear Algebra (MTH-SHU 140) Homework 5

2020/03/18

The Lecturer

Name

Instructions. Please write down your answers in details.

Let R denote the set of real numbers.

1. Are the following sets vectors spaces? Justify your answers.

(1) V = f(x; y) j x

(2) f(x; y) j xy

0; y

0g;

0g;

(3) A subset V of Rn containing 0:

(4) All polynomials of the form ax2 ; where a 2 R:

(5) The set of all polynomials with integers as coe¢ cients.

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2. Determine whether the following sets are bases of R3 . Give proofs.

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3. Two vector spaces V; W are called isomorphic if there is a bijective linear map T : V ! W:

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4. Is the following each statement true or false? If false, write F and give counter examples. If

true, write T and give brief explainations.

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