Let W be a subspace of Rn and v a vector in Rn. Suppose that w and w' are orthogonal vectors with winW and that v = w + w'.Is it necessarily true that w' is in W~L? Either prove that it is true or find a counterexample.

Let W be a subspace of Rn and v a vector in Rn. Suppose that w and w' are orthogonal vectors with winW and that v = w + w'.Is it necessarily true that w' is in W~L? Either prove that it is true or find a counterexample.

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 41CR: Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the...

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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.

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Let W be a subspace of Rⁿ and v a vector in Rⁿ. Suppose that w and w' are orthogonal vectors with winW and that v = w + w'.Is it necessarily true that w' is in W~L? Either prove that it is true or find a counterexample.

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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