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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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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