Mathematics II - Old Questions

16. Determine if the following system is inconsistent.

x₂ - 4x₃ = 8

2x₁ - 3x₂ + 2x₁ = 1

5x₁ - 8x₂ + 7x₃ = 1

OR

Let a₁ = (1, -2, -5), a₂ = (2, 5, 6) and b = (7, 4, -3) are the vectors. Determine whether b can be generated as a linear combination of a₁ and a₂. That is determine whether x₁ and x₂ exist such that x₁a₁ + x₂a₂ = b has solution, find it.