mat all the diagonal enteries ofA are non-zero, then the column vectors of A are linearly independent. 2. Let S = {s1, $2, 83, S4}, where s% = , S2 = 0. and S4 = , 83 = (i) Find the value(s) of c for which S is linearly dependent. (ii) Prove that the answer in (i) is correct by obtaining a nonzero vector such that 3 4. aS; = 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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help with 2.i and ii

Che diagonal enterieS of A are non-zero,
then the column vectors of A are linearly independent.
-2
2. Let S = {S1, $2, S3, S4}, where s1 =
0.
and S4=
S2 =
S3 =
(i) Find the value(s) of c for which S is linearly dependent.
03
(ii) Prove that the answer in (i) is correct by obtaining a nonzero vector
such that
O;S; =
0.
2=1
Transcribed Image Text:Che diagonal enterieS of A are non-zero, then the column vectors of A are linearly independent. -2 2. Let S = {S1, $2, S3, S4}, where s1 = 0. and S4= S2 = S3 = (i) Find the value(s) of c for which S is linearly dependent. 03 (ii) Prove that the answer in (i) is correct by obtaining a nonzero vector such that O;S; = 0. 2=1
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