precalculus matrices

Question

Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, do the following. (Use x₁, x₂, x₃, and x₄, as your variables, each representing the columns in turn.)

	1	0	3	−1	4
0	1	−2	3	6
0	0	0	0	0
0	0	0	0	0

Answer 1

x₁ + 3x₃ - x₄ = 4

x₂ - 2x₃ + 3x₄ = 6

x₃ and x₄ are parameters (any real numbers)

If we let x₃ = s and x₄ = t, then:

x₁ = -3s + t + 4

x₂ = 2s - 3t + 6

x₃ = s

x₄ = t

Solutions: (x_{1 ,} x_2, x_3, x₄) = s(-3, 2, 1, 0) + t(1, -3, 0, 1) + (4, 6, 0, 0), where s and t are any real numbers