Let A = 1 -1 -S 1 -S 1 S 1 Study how the nullspace of A, denoted Nul A depends on the parameter s. For which values of s (if any) is the nullspace of A: (i) a line through the origin? (ii) a plane through the origin? (iii) the origin only? Find an equation of the plane in case (ii).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let
A =
1 S
-1 -S -1
-1 -1
-S
Study how the nullspace of A, denoted Nul A depends on the parameter s. For which values
(if any) is the nullspace of A: (i) a line through the origin? (ii) a plane through the
origin? (iii) the origin only? Find an equation of the plane in case (ii).
of s
Remark. This is a bonus problem. Note that only correct computations and correct answers
with motivation will give credit (in particular, you may not receive partial credit if the compu-
tations are wrong). So, be concentrated.
Transcribed Image Text:Let A = 1 S -1 -S -1 -1 -1 -S Study how the nullspace of A, denoted Nul A depends on the parameter s. For which values (if any) is the nullspace of A: (i) a line through the origin? (ii) a plane through the origin? (iii) the origin only? Find an equation of the plane in case (ii). of s Remark. This is a bonus problem. Note that only correct computations and correct answers with motivation will give credit (in particular, you may not receive partial credit if the compu- tations are wrong). So, be concentrated.
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