Can someone help me with this question please :) (University)

(-5 1 0 0) and (-3 0 1 0)

Step-by-step explanation:

Based on my memory,  you can use the dot product to find orthogonality meaning

u1 . u2 = 0

In this case, we let u be the arbitrary vector represented by (x y z w)

u . (1 5 3 0) can be expressed as an equation given by:

{(x y z w) | x + 5y + 3z  + 0w= 0}

We solve this equation letting y = s and z = t and x = -5s -3t

Reconstruct this according to their variable will give

(-5 1 0 0)s + (-3 0 1 0)t = 0

So the basis vectors are (-5 1 0 0) and (-3 0 1 0).

Let c1 and c2 be arbitrary constants:

if you solve for c1(-5 1 0 0) + c2(-3 0 1 0) = 0

c1 and c2 should have only trivial solution, which proves its

linear independence and so it forms a basis vector space.

sine

step-by-step explanation: