Consider the following two bases for R^3

fortdefruitI

fortdefruitI

Answered question

2020-11-02

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).

Answer & Explanation

Pohanginah

Pohanginah

Skilled2020-11-03Added 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]

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?