Homework SourseFind a basis for the set of vectors vx y z in R3 that satisf
Find a basis for the set of vectors v=[x y z] in R^3 that satisfy the equation 5x+6y-2z=0
Solution
Let v= ( x, y, z) (1)
given 5x+6y-2z=0
5x = - 6y + 2z
x = -6y/5 + 2z/5 (2)
Put value of x from (2) into (1), we get
v= ( -6y/5 + 2z/5 , y ,z ) = ( -6y/5 + 2z/5 , y + 0.z, 0.y + z ) = y ( -6/5 , 1 , 0 ) +z ( 2/5 , 0 , 1 )
Hence, basis is { ( -6/5 , 1 , 0 ) , ( 2/5 , 0 , 1 ) }.
![Find a basis for the set of vectors v=[x y z] in R^3 that satisfy the equation 5x+6y-2z=0SolutionLet v= ( x, y, z) (1) given 5x+6y-2z=0 5x = - 6y + 2z x = -6y/5](/WebImages/26/find-a-basis-for-the-set-of-vectors-vx-y-z-in-r3-that-satisf-1066467-1761557925-0.webp "Find a basis for the set of vectors v=[x y z] in R^3 that satisfy the equation 5x+6y-2z=0SolutionLet v= ( x, y, z) (1) given 5x+6y-2z=0 5x = - 6y + 2z x = -6y/5")
