OCME · Bilingual mathematics & derivations
Concept derivation guides
299 concept teaching guides, separate from the 36,000 individual question derivations.
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Concept guide
In the fixed standard basis let u=(3,−1), v=(−2,4), w=(1,3) and k=−2. Compute u+v, u−v, v−u, ku, 0u and 2u+v componentwise; find the vector x with u+x=v; check k(u+v)=ku+kv; and decide whether u=w and whether u=(−1,3).
Plane vectors in a fixed basis
derivation-mko-vector-01
Concept guide
U={(x,2x):x in R} is a subspace of R2, whereas U+(0,1) is not.
Real vector subspace
derivation-mko-vector-subspace-01
Concept guide
B=((1,1),(1,-1)) is an ordered basis of R2, so dim R2=2.
Dimension of a finite-dimensional vector space
derivation-mko-vector-space-dimension-01