IF THESE ARE LINERLY INDEPENDENT FIND ONLY THE SCALARS THAT

IF THESE ARE LINERLY INDEPENDENT, FIND ONLY THE SCALARS THAT WILL MAKE THE EQUATION ABOVE TRUE.

Solution

let

a[5 -5 2] + b[1 3 0] + c[-1 -4 -4] = [0 0 0]

=>

5a +b -c = 0

-5a+3b-4c = 0

2a-4c = 0 => a = 2c =>b = -9c => -5(2c) +3(-9c) -4c = -41c = 0 => c = 0

=>
a = b = c = 0

the only scalars that will make the given equation is

(0,0,0)