Linear Algebra Questions Exam Practice

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.
1
2. Determine whether the following sets are bases of R3 . Give proofs.
2
3. Two vector spaces V; W are called isomorphic if there is a bijective linear map T : V ! W:
3
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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