Question

1.) either solve the given system of equations, or else show that there is no solution.

x₁ + 2x₂ - x₃ = 2

2x₁ + x₂ + x₃ = 1

x₁ - x₂ + 2x₃ = -1

2.) determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them.

(a.) x⁽¹⁾ = (1, 1, 0) , x⁽²⁾ = (0, 1, 1) , x⁽³⁾ = (1, 0, 1)

(b.) x⁽¹⁾ = (2, 1, 0) , x⁽²⁾ = (0, 1, 0) , x⁽³⁾ = (-1, 2, 0)

Answer 1

This linear algebra problem can be solved in this way