Are the vectors v 13 and u 2 61 a basis for R2SolutionGive

Are the vectors v = (1,3) and u = (2, 6.1) a basis for R²?

Solution

Given that

v = ( 1 , 3 ) and u = ( 2 , 6.1 )

c x ( 1, 3 ) ( 2 ,6.1)

Where c = constant

v c x u

Hense,

v , u are not multiples of each other

Then v,u are linearly independent

Therefore,

v , u are forms a basis for R2