3. Consider the problem of determining whether the following system of equations is 2x1 - 4x2 – 2x3 = b, -5x1 + x2 + x3 = b2 7x1 - 5x2 - 3x3 = b3 consistent for all b, b2, b3: a) Define appropriate...

Extracted text: 3. Consider the problem of determining whether the following system of equations is 2x1 - 4x2 – 2x3 = b, -5x1 + x2 + x3 = b2 7x1 - 5x2 - 3x3 = b3 consistent for all b, b2, b3: a) Define appropriate vectors and restate the problem in terms of Span {v,, 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.