3) Consider R³ and let W be the subspace that contains all vectors on the planex + 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 equationsand 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 ontoW.

Answered: Image /qna-images/answer/2d6164d4-917a-4d97-9599-833c32ca4e8f.jpg

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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 33EQ

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