MATHS-LINEAR ALGEBRA

[drishtinarula]

1.SUPPOSE V1,V2 AND V3 ARE THREE VECTORS IN 3D SPACE, AND ARE LINEARLY DEPENDENT. THEN THE VECTORS V1+V2, V2+V3, V1+V3 ARE
LINEARLY DEPENDENT
MAY BE LINEARLY DEPENDENT
ARE LINEARLY DEPENDENT
ARE LINEARLY DEPENDENT, EXCEPT WHEN ONE OF THE VECTORS IS ZERO.

[Asd1995]

v1= k*v2 plus j*v3 (given)

substitute above into v1 plus v2= (k plus 1)*v2 plus j*v3= can be written as a linear combination of v2 plus v3 and v1 plus v3  (messy stuff, proceed by writing v1 again from the first formula)

so they're always dependent.