I am trying to write the vector v=(2,3) in the basis outlined by the set {(−1,1),(3,−5)}. I figured that I would take the inverse of the set matrix, and multiply it to v. However, this does not seem to be the solution. Any help would be greatly appreciated.

ximblajy

ximblajy

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2022-08-21

I am trying to write the vector v = ( 2 , 3 ) in the basis outlined by the set { ( 1 , 1 ) , ( 3 , 5 ) }. I figured that I would take the inverse of the set matrix, and multiply it to v. However, this does not seem to be the solution. Any help would be greatly appreciated.

Answer & Explanation

Keely Blankenship

Keely Blankenship

Beginner2022-08-22Added 6 answers

Define v 1 = ( 1 , 1 ) , v 2 = ( 3 , 5 ) and the vector of coefficients as (a,b). Hence you must have
v = ( a , b ) [ v 1 v 2 ]
which leads to
v [ v 1 v 2 ] 1 = ( a , b )

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