Mathematics II - Old Questions

16. Let a₁ = (1, 2, -5), a₂ = (2,5,-3) and b = (7,4, -3). Determine whether b can be generated as a linear combination of a₁ and a₂. That is, determine whether x₁ and x₂ exists such that x₁a₁ + x₂a₂ = b

has the solution , find it.

OR

Determine if the following system is consistent

x₂ - 4x₃ = 8

2x₁ - 3x₂ + 2x₃ = 1

5x₁ - 8x₂ + 7x₃ = 1