I need help solving this (

Question

The solution set of the linear system:

w-3x+4y-3z=-5

-w+8x-4y+18z=15

may be written as{v1+sv2+tv3} for some vectors v1, v2 and v3. Find v1, v2 and v3 using that equation

Answer 1

w - 3x + 4y - 3z = -5

-w + 8x - 4y + 18z = 15

Add the equations to get 5x + 15z = 10 So, x + 3z = 2.

w - 3x + 4y - 3z = -5

x + 3z = 2

Add 3 times the second equation to the first:

w + 4y + 6z = 1

x + 3z = 2

So, x = -3z + 2

w = -4y - 6z + 1

y = any real number (let y = s)

z = any real number (let z = t)

(w, x, y, z) = (-4s - 6t + 1, -3t + 2, s, t) = (1, 2, 0 ,0) + s(-4, 0, 1, 0) + t(-6, -3, 0, 1)