Let matrix A represent an orthogonal projection onto the subspace V, where V is the plane x + 2y + 3z = 0 in R3. a) Find a basis of im(A). b) Find a basis of ker(A). c) Find the orthogonal projection of the vector ⃗v = [1 2 3] onto V

Let matrix A represent an orthogonal projection onto the subspace V, where V is the plane x + 2y + 3z = 0 in R3. a) Find a basis of im(A). b) Find a basis of ker(A). c) Find the orthogonal projection of the vector ⃗v = [1 2 3] onto V

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter1: Vectors

Section1.3: Lines And Planes

Problem 47EQ

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Question

Let matrix A represent an orthogonal projection onto the subspace V, where V is the plane x + 2y + 3z = 0 in R3.

a) Find a basis of im(A).
b) Find a basis of ker(A).

c) Find the orthogonal projection of the vector ⃗v = [1 2 3] onto V

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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