Final answer:
To find the solution set of the system of equations in parametric vector form, you perform row reduction on the system's matrix to find out that x₃ can be a free parameter. Then, express x₁ and x₂ in terms of x₃, and write the solution set with x₃ as the parameter.
Step-by-step explanation:
To find the solution set of the given homogeneous system of equations in parametric vector form, we need to solve the system:
- x₁ +3x₂ −5x₃ = 0
- x₁ +4x₂ −8x₃ = 0
- −3x₁ −7x₂+ 9x₃ = 0
Let's express the system in matrix form and perform row reduction to echelon form.
After simplifying, you might end up with a matrix that looks something like this:
[1 0 a
0 1 b
0 0 0]
This suggests that x₃ (the third variable) can be a free parameter, for example, let x₃ = t.
Now, we can express x₁ and x₂ in terms of t using the first two equations:
x₁ = -at
x₂ = -bt
Thus, in parametric vector form, the solution set is:
t(-a, -b, 1)
where R is the set of all real numbers.