Consider the problem of determining whether the following

Question

Question: Consider the problem of determining whether the following system of equations is consistent for all b1, b2, b3:

2x₁ - 4x₂ - 2x₃ = b₁

-5x₁ + x₂ + x₃ = b₂

7x₁ - 5x₂ - 3x₃ = b₃

a. Define appropriate vectors, and restate the problem in terms of Span {v1, v2, v3}. Then solve that problem.

b. Define an appropriate matrix, and restate the problem using the phrase "columns of A."

c. Define an appropriate linear transformation T using the matrix in (b), and restate the problem in terms of T.