Answered: Let V = U® W and let {u̟,u2, ... , uk }…

Let V = U® W and let {u̟,u2, ... , uk } be a basis for the subspace U and {W1,W2, ..., Wk } be a basis for the subspace W. Prove that the set {U1,U2, ... , Uk , W1, W2, ... ,Wk } is a basis for V.

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

Let V = UÐ W and let {u1,U2, ... , Uk } be a basis for the subspace U and
{w1, W2, ... , Wk } be a basis for the subspace W.
Prove that the set {u1,u2, ... , uk, W1, w2, ... , Wk } is a basis for V.
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