) The points (1, 0, 3), (1, 1, 1), and (−2, −1, 2) lie on a unique plane a1x1 + a2x2 + a3x3 = b. Using your previous answers, find an equation for this plane. (Hint: think about the relationship between the previous system and the one you would need to solve in this question.)

2x₁ - x₂ + x₃ = 2

Question in full

(a) Find the general solution for the following system of linear equations:

z2 + 3z3 − z4 = 0

−z1 − z2 − z3 + z4 = 0

−2z1 − 4z2 + 4z3 − 2z4 = 0

(b) Give an example of a solution to the previous system of linear equations.

(c) The points (0, 1, 3), (1, 1, 1), and (−1, −2, 2) lie on a unique plane in R 3 , defined by an equation of the form a1x1 + a2x2 + a3x3 = b. Using your previous answers, find an equation for this plane. (Hint: think about the relationship between the previous system and the one you would need to solve in this question.)

Step-by-step explanation:

The augmented matrix is

The echelon form

The general solution and the sample solution

as well as the equation of the plane

are given in the attached solution below

7

step-by-step explanation: