Find the best approximation to z by vectors of the form c_1v_1+c_2v_2

Amari Flowers

Amari Flowers

Answered question

2021-09-24

Find the best approximation to z by vectors of the form c1v1+c2v2
z=[3723], v1=[2131] v2=[1101]

Answer & Explanation

2abehn

2abehn

Skilled2021-09-25Added 88 answers

Find the best approximation to z by vectors of the form c1v1+c2v2
z=[3723], v1=[2131] v2=[1101]
The formula of orthigonal projection of z onto span v1,v2 and this projection is the best approximiation to z by vectors c1v1+c2v2
because z,v1=10,v1v1=15,zv2=7, v2v2=3
z^=1015[2131]+73[1101]
The required best approximation to z by vectors c1v1+c2v2
z^=[1323]
Result:
z^=1015[2131]+73[1101]=[1323]

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