Consider the basis B of R2 consisting of vectors

5

-6

and

-2

-2

Find x in R2 whose coordinate vector relative to the basis B is

[x]B = [-6]

[ 2 ]

Question

Mathematics

Yaretzi Baird

1 June, 07:34

Consider the basis B of R2 consisting of vectors

5

-6

and

-2

-2

Find x in R2 whose coordinate vector relative to the basis B is

[x]B = [-6]

[ 2 ]

+4

Answers (1)

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Tabitha · Answer 1

The idea is to find a linear combination a_1 (5, - 6) + a_2 (-2, - 2) = (-6, 2) It boils down to a system of equations: Take the augmented matrix:

[ 5 - 6 - 2 - 2 - 6 2 ] Reduced form: [ 10 01 - 811 1311 ] - (8/11) * (5, - 6) + (13/11) * (-2, - 2) = (-6, 2)

Consider the basis B of R2 consisting of vectors5-6and-2-2Find x in R2 whose coordinate vector relative to the basis B is[x]B = [-6][ 2 ]

Consider the basis B of R2 consisting of vectors

5

-6

and

-2

-2

Find x in R2 whose coordinate vector relative to the basis B is

[x]B = [-6]

[ 2 ]