(c) Let V be the vector space of all 2 x 2 complex matrices over R. Consider -{[ 0 a11,922 ER (iii) (iv) W = 0 a22 If now V is a vector space of all 2 x 2 complex matrices over C, explain whether W is still a subspace of V. If now V is a vector space of all 2 x 2 complex matrices over C and W is assumed to be a subspace of V, then determine the dimension of W.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(c)
Let V be the vector space of all 2 x 2 complex matrices over R. Consider
-{[
(iii)
(iv)
W =
0
0
a22
a11,922 ER
a
If now V is a vector space of all 2 x 2 complex matrices over C, explain
whether W is still a subspace of V.
If now V is a vector space of all 2 x 2 complex matrices over C and W is
assumed to be a subspace of V, then determine the dimension of W.
Transcribed Image Text:(c) Let V be the vector space of all 2 x 2 complex matrices over R. Consider -{[ (iii) (iv) W = 0 0 a22 a11,922 ER a If now V is a vector space of all 2 x 2 complex matrices over C, explain whether W is still a subspace of V. If now V is a vector space of all 2 x 2 complex matrices over C and W is assumed to be a subspace of V, then determine the dimension of W.
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