(a) Find the bases and dimension for the subspace

ossidianaZ 2021-01-31 Answered

(a) Find the bases and dimension for the subspace H={[3a+6bc6a2b2c9a+5b+3c3a+b+c];a,b,cR} (b) Let be bases for a vector space V,and suppose (i) Find the change of coordinate matrix from B toD. (ii) Find [x]Dforx=3b12b2+b3

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Expert Answer

okomgcae
Answered 2021-02-01 Author has 93 answers

a) v1=[3693],v2=[6251],v3=[1231] Then H= v1,v2,v3
[361622953311][36101400230070]by{R22R1R3+3R1R4+R1
[361010000000]by{114R2R323R2R47R2 This shows that the vectors

v1=[3693],v2=[6251] are linearly independent and thus form bases for the given subspace. Simiarly v2=[6251],v3=[1231] also form basis for the set H, dimesion of the space is

2. b) Find the change of coordinate matrix from B to D. PDB=[203130112]

Find [x]Dforx=3b12b2+b3.
[x]D=[203130112][321]=[393]

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