MATH 307 Lecture Notes - Lecture 16: Init
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E s 2x 12 2 21 1 4 0 es. Yg es 2ep xity 1khz xi1 2 1 titta o. S is a subspace of1133 actually sis a linein. 1 so s fat o it 3 xit. O s f1 ix x er em aplanein r. Def alinear combination ofvectors vi v2 ukis for some cl. Iii lil 111 il il iii iti n111 1 1 i. If vi ukarelinearlydependent clut it ckvk ewherenotallci"sarezero saygto. Ij civ1 it cj avj it cj11vj11 t. Def thevectorsvi ukare linearlyindependent if i ciri 8 implies 01 02 i ck. 1 forth uk if thereexists vi 2vjforsomeviandvj 7 l vi nj o linearlydependent vi nj onthesameline. Thenthereexists p 2 with v burt2b so it v na b er2 theyarelinearly dependent l vi bir 2b i 7 linearlydependent. Zerovectoristheunique solution toc a linearly dependent some cite. Thereare 2possiblecases depending on n andk w ofvectors w sizeof vector.
