Problem 2. Consider vector space V over field R. Consider linearly independent sequence (v₁, V₂,..., Un) from V, where n ≤ dim(V). Then the set (v₁, V2,..., Un) is a basis of vector space V. a) b) d) has dimension n. is equal to V. is a vector space over R.

Problem 2. Consider vector space V over field R. Consider linearly independent sequence (v₁, V₂,..., Un) from V, where n ≤ dim(V). Then the set (v₁, V2,..., Un) is a basis of vector space V. a) b) d) has dimension n. is equal to V. is a vector space over R.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

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

Consider vector space V over field R. Consider linearly independent
sequence (v₁, v₂, . . . , v_n) from V , where n ≤ dim(V ). Then the set <v₁, v₂ ,. . . , v_n>
a) is a basis of vector space V .
b) has dimension n.
c) is equal to V .
d) is a vector space over R.

Problem 2.
Consider vector space V over field R. Consider linearly independent
sequence (v1, v2,... , Vn) from V, where n < dim(V). Then the set (v1, v2, . ..,
а)
is a basis of vector space V.
b)
has dimension n.
is equal to V.
d)
is a vector space over R.

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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