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Redraw Figure 4.3 for a 3 by 2 matrix of rank r 2. Which subspace is Z (zero vector only)? The nullspace part of any vector æ in R2 is æn

Redraw Figure 4.3 for a 3 by 2 matrix of rank r 2. Which subspace is Z (zero vector only)? The nullspace part of any vector æ in R2 is æn

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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Redraw Figure 4.3 for a 3 by 2 matrix of rank r = 2. Which subspace is Z (zero vector only)? The nullspace part of any vector x in R² is n =
Transcribed Image Text:Redraw Figure 4.3 for a 3 by 2 matrix of rank r = 2. Which subspace is Z (zero vector only)? The nullspace part of any vector x in R² is n =
dim r all combinations of the rows R" all vectors orthogonal to the rows dim n-r Ax,-b Ax=b all combinations b of the dim r columns R Ax=0 all vectors orthogonal to the columns dim m-r Figure 4.3: This update of Figure 4.2 shows the true action of A on x = x + In- Row space vector + to column space, nullspace vector л to zero.
Transcribed Image Text:dim r all combinations of the rows R" all vectors orthogonal to the rows dim n-r Ax,-b Ax=b all combinations b of the dim r columns R Ax=0 all vectors orthogonal to the columns dim m-r Figure 4.3: This update of Figure 4.2 shows the true action of A on x = x + In- Row space vector + to column space, nullspace vector л to zero.
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