(a) Let (1 0 1 D = | 2 1 0 1 1 Find the matrix of cofactors (signed minors) of D and use this to find D-1 if it exists. Show all work.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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8. (a) Let
1 0 1
D = 2 1 0
1 1 1
Find the matrix of cofactors (signed minors) of D and use this to find D-1
if it exists. Show all work.
(b) Let ~ be the relation on C defined by z ~ w if and only if z + w € R.
Prove that - is an equivalence relation.
(c) Let X be the set of non-zero complex numbers and let - be the relation
on X defined by z ~ w if and only if zu e R. Given that - is an
equivalence relation on X, describe the ~-equivalenc
[1] = [2]?
[2 – 3i]. Is
Transcribed Image Text:8. (a) Let 1 0 1 D = 2 1 0 1 1 1 Find the matrix of cofactors (signed minors) of D and use this to find D-1 if it exists. Show all work. (b) Let ~ be the relation on C defined by z ~ w if and only if z + w € R. Prove that - is an equivalence relation. (c) Let X be the set of non-zero complex numbers and let - be the relation on X defined by z ~ w if and only if zu e R. Given that - is an equivalence relation on X, describe the ~-equivalenc [1] = [2]? [2 – 3i]. Is
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