Which of the following are subspaces of R3, if it is not explain briefly why not. (a) The zero vector (b) The line through (1,2, 3) and (0,0,0) (c) The line through (1, 2, 3) and (4,5, 6) (d) The mlome 7. 77uI 777. -0

Which of the following are subspaces of R3, if it is not explain briefly why not. (a) The zero vector (b) The line through (1,2, 3) and (0,0,0) (c) The line through (1, 2, 3) and (4,5, 6) (d) The mlome 7. 77uI 777. -0

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 73CR

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Which of the following are subspaces of R3, if it is not explain briefly why not.
(a) The zero vector
(b) The line through (1,2, 3) and (0,0,0)
(c) The line through (1, 2, 3) and (4, 5, 6)
(d) The plane 7x + 77y + 777z = 0
(e) A sphere of radius 1 centered at (1,0, 0)
(f) The yz-plane (i.e. x=0)

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