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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?

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?

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 29CM
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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?
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