3. (.(a) i. (:3) Let X = {(v1, v2, v3) E R* | v1 – v2 = v3}.Determine whether X is a subspace of R$ or not.ii. (. , Let Y = {(u1, u2, U3) E R| u1 – u2Determine whether Y is a subspace of R° or not.-1}U3 = -(b) Consider the equation of the plane P: 2x–- 3y + 4z = 0 in R³.i. (:'s) The plane P is the nullspace of some matrix A. Find the entries of A.:) Find a basis for the nullspace of the matrix A.ii. (.iii. ( ) Find a basis for the plane P.

To solve the following problem, we use the following defination of subspace.

i. ( : ) Let X = {(v1, v2, V3) E R* | v1 – v2 = v3}. Determine whether X is a subspace of R³ or not. ii. (. ;, Let Y = {(u1, U2, U3) E R³ | u1 u2 – u3 = -1} Determine whether Y is a subspace of R³ or not.

i. ( : ) Let X = {(v1, v2, V3) E R* | v1 – v2 = v3}. Determine whether X is a subspace of R³ or not. ii. (. ;, Let Y = {(u1, U2, U3) E R³ | u1 u2 – u3 = -1} Determine whether Y is a subspace of R³ or not.

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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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

3. (.
(a) i. (:3) Let X = {(v1, v2, v3) E R* | v1 – v2 = v3}.
Determine whether X is a subspace of R$ or not.
ii. (. , Let Y = {(u1, u2, U3) E R| u1 – u2
Determine whether Y is a subspace of R° or not.
-1}
U3 = -
(b) Consider the equation of the plane P: 2x–- 3y + 4z = 0 in R³.
i. (:
's) The plane P is the nullspace of some matrix A. Find the entries of A.
:) Find a basis for the nullspace of the matrix A.
ii. (.
iii. ( ) Find a basis for the plane P.

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