Answered: Which of the following are vector…

Which of the following are vector subspaces of of IR³? a) all vectors of the form (a, b, c), where b = a + c? b) all vectors of the form (a, b, c), where b = a + c + 1?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...

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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 vector subspaces of R³^?

all vectors of the form (a, b, c), where b = a + c?
all vectors of the form (a, b, c), where b = a + c + 1?

Note: In the image the problem is described more clearly, do not skip any step and solve the two parts a and b.

Which of the following are vector subspaces of of R ?
a) all vectors of the form (a, b, c), where b = a + c?
b) all vectors of the form (a, b, c), where b = a + c + 1?

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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