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3) Consider R³ and let W be the subspace that contains all vectors on the plane x + y = 0. Answer the following questions: 3.1) Find a basis for W. 3.2) Let b e R³ with b = (b1, b2, b3). Write down a linear system of three equations and two unknowns, say x1 and x2, that needs to be satisfied for b E span{W}. 3.3) Write the system in 3.2) in the matrix form A = b, where = (x1, x2). 3.4) Find the standard matrix for the orthogonal projection of a vector č E R³ onto W.

3) Consider R³ and let W be the subspace that contains all vectors on the plane x + y = 0. Answer the following questions: 3.1) Find a basis for W. 3.2) Let b e R³ with b = (b1, b2, b3). Write down a linear system of three equations and two unknowns, say x1 and x2, that needs to be satisfied for b E span{W}. 3.3) Write the system in 3.2) in the matrix form A = b, where = (x1, x2). 3.4) Find the standard matrix for the orthogonal projection of a vector č E R³ onto W.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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3) Consider R³ and let W be the subspace that contains all vectors on the plane x + y = 0. Answer the following questions: 3.1) Find a basis for W. 3.2) Let b e R³ with b = (b1, b2, b3). Write down a linear system of three equations and two unknowns, say xị and x2, that needs to be satisfied for b E span{W}. 3.3) Write the system in 3.2) in the matrix form Ar = b, where = (x1, 02). 3.4) Find the standard matrix for the orthogonal projection of a vector č E R³ onto W.
Transcribed Image Text:3) Consider R³ and let W be the subspace that contains all vectors on the plane x + y = 0. Answer the following questions: 3.1) Find a basis for W. 3.2) Let b e R³ with b = (b1, b2, b3). Write down a linear system of three equations and two unknowns, say xị and x2, that needs to be satisfied for b E span{W}. 3.3) Write the system in 3.2) in the matrix form Ar = b, where = (x1, 02). 3.4) Find the standard matrix for the orthogonal projection of a vector č E R³ onto W.
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