(a) Let V = {(Z, Z2, Z3)|Z{ e C} = c* be the vector space over C. Check whether W= {(Z,, Z2, Z3) |Z, + Z2 = 1} are subspaces of V or mt. (b) W= {(x, x2, x3) € R | x1 - 2x2 + 3x3 = 0} are subspaces of R³ or ot.

(a) Let V = {(Z, Z2, Z3)|Z{ e C} = c* be the vector space over C. Check whether W= {(Z,, Z2, Z3) |Z, + Z2 = 1} are subspaces of V or mt. (b) W= {(x, x2, x3) € R | x1 - 2x2 + 3x3 = 0} are subspaces of R³ or ot.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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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.

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Q.1.
(a) Let V = {(Z, Z2, Z3) |Z{ e C} = C³ be the vector space over C. Check whether
W= {(Z, Z2, Z3) |Z, + Z2 =1} are subspaces of V or mt.
(b)
W= {(x1, x2, x3) € R³ | x1 - 2x2 + 3x3 = 0} are subspaces of R³ or ot.

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