Linear Algebra Done Right · Problem 1C.20

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · direct-sums

Problem

Suppose U={(x,x,y,y)∈F4:x,y∈F}.U = \{(x, x, y, y) \in \mathbf{F}^4 : x, y \in \mathbf{F}\}. Find a subspace WW of F4\mathbf{F}^4 such that F4=U⊕W\mathbf{F}^4 = U \oplus W.

Related theory

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