Linear Algebra Done Right · Problem 1C.21

Finite-Dimensional Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · direct-sums

Problem

Suppose U={(x,y,x+y,x−y,2x)∈F5:x,y∈F}.U = \{(x, y, x+y, x-y, 2x) \in \mathbf{F}^5 : x, y \in \mathbf{F}\}. Find a subspace WW of F5\mathbf{F}^5 such that F5=U⊕W\mathbf{F}^5 = U \oplus W.

Related theory

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