Math 54 quiz 1 find all solutions to the following system

Question

MATH 54 QUIZ 1-

1. Find all solutions to the following system of equations. Write your answer in parametric vector form.

x₂ + 2x₃ = 5

2x₁ + 6x₂ + x₃ = 9

-x₁ - x₂ + 3x₃ = 4

3x₁ + 5x₂ - x₃ = 10

2. Give an example of a matrix that is not in echelon form. Give an example of a matrix that is in echelon form but is not in reduced echelon form.

3. Do the columns of A =span R³? Justify your answer.

4. Let v₁, v₂, v₃ and w be four vectors in R³. Suppose that w ∈ Span{v₁, v₂, v₃}. Prove that w ∈ Span{v₁ + v₂, v₂, v₃}.

5. Write anything you like here (comments, questions, suggestions, etc).