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

Transcribed Image Text:

2x14x22x3 = b₁ -5x1 + x₂ + x3 = b₂ 7x15x2 3x3 = b3 -