Question

Let U ⊂ C4 be the subspace U = {(z1, z2, z3, z4) ∈ C4: z1 + z2 + z3 + z4 = 0 and z1 = iz2}.

(a) Find a basis for U. What is dim U?
(b) Extend the basis from part (a) to a basis for C4.

(c) Find a subspace W ⊂ C4 such that C4 = U ⊕ W. What is dim W?

Answer 1

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Consides the matrix o A z -I incaly Yank A- Sinu u, and u independint null spa c A, Considu NCA)2:AZ we conside vechog Column vterely C2,, 2, 2, Zu) ENCA) 2 A z o hen o i- O t2, and2, +Z2+ i-) 2,-0 -i2,ti)23 23 23 basis NCA) an - '

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