Construct any 2 by 3 matrix of rank one. Copy Figure 4.2 and put one vector in each subspace (and put two in the nullspace). Which vectors are orthogonal?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
Problem 1EQ: Draw the following vectors in standard position in 2 : aa=30bb=23cc=23dd=32
icon
Related questions
Question

I need help with this please

dimension
row
space
of A
row space to column space
Axrow = b
column
space
of A
R"
90°
90°
nullspace
of A
Axnull =0
nullspace to 0
nullspace
of AT
dimension
=n-r
dimension
=m-r
dimension
Figure 4.2: Two pairs of orthogonal subspaces. The dimensions add to n and add to m.
This is the Big Picture-two subspaces in R" and two subspaces in R™.
Transcribed Image Text:dimension row space of A row space to column space Axrow = b column space of A R" 90° 90° nullspace of A Axnull =0 nullspace to 0 nullspace of AT dimension =n-r dimension =m-r dimension Figure 4.2: Two pairs of orthogonal subspaces. The dimensions add to n and add to m. This is the Big Picture-two subspaces in R" and two subspaces in R™.
Construct any 2 by 3 matrix of rank one. Copy Figure 4.2 and put one vector in each
subspace (and put two in the nullspace). Which vectors are orthogonal?
Transcribed Image Text:Construct any 2 by 3 matrix of rank one. Copy Figure 4.2 and put one vector in each subspace (and put two in the nullspace). Which vectors are orthogonal?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,