Consider the following two bases for R^3

fortdefruitI 2020-11-02 Answered

Consider the following two bases for R3 :
α:={[213],[101],[311]}and β:={[111],[231],[231]} If [x]α=[121]αthen find [x]β
(that is, express x in the β coordinates).

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Expert Answer

Pohanginah
Answered 2020-11-03 Author has 96 answers

α={[213],[101],[311]}β={[111],[231],[231]}
[x]α=[121]αx=1.[213]+2[101]1[311]=[306] Let x=C1[111]+C2[231]+C3[231]C12C2+2C3=3(1)C1+3C+2+3C3=0(2)C1+C2C3=6(3) From (3) C3=C1+C26 From (1) C12C2+2C1+2C212=33C1=+9C1=3 From (2) C1+3C2+3C1+3C218=04C1+6C2=186C2=C2
C3=3+16=2 So [306]=+3[111]+1[231]2[231] So [x]β=[312]

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